53380:nwmsexch:mapi(1295): Insufficient permissions to access mailbox

Error status: 0x8004011d

Above seems to be typical permission problem with mailbox store... check docs and KB for more details on permission requirements.

The following permissions be set, but still can't backup: OpenMsgStore() = 0x8004011d:
¿ List contents
¿ Read properties
¿ Administer Information Store
¿ View Information Store status
¿ Receive as
¿ Send as

If I don't understand wrong you are trying to do a backup from NetWorker User for Exchange when you obtain this error, is it?
If yes which is the user what you are logged? Has it the right permissions?
Have you tried to do a Backup Server initiated backup to Exchange MB?

[5744] 11/27/07 14:11:26 Start time Tue Nov 27 14:11:26 2007
[5188] 11/27/07 14:11:26 Computer Name: MAILSRV User Name: GOCT\administrator (administrator)
[5744] 11/27/07 14:11:26 Computer Name: MAILSRV User Name: GOCT\administrator (administrator)
[5188] 11/27/07 14:11:26 nsrxchsv_ese.exe Version: 4.1.0.148 Supporting Exchange 2000 and Exchange 2003
[5188] 11/27/07 14:11:26 System Version: 5.2 Build 3790 Service Pack 1
[5744] 11/27/07 14:11:26 nsrxchsv_ese.exe Version: 4.1.0.148 Supporting Exchange 2000 and Exchange 2003
[5744] 11/27/07 14:11:26 System Version: 5.2 Build 3790 Service Pack 1

[5356] 11/27/07 14:11:26 Start time Tue Nov 27 14:11:26 2007
[5356] 11/27/07 14:11:26 Computer Name: MAILSRV User Name: GOCT\administrator (administrator)
[5356] 11/27/07 14:11:26 nsrxchsv_ese.exe Version: 4.1.0.148 Supporting Exchange 2000 and Exchange 2003
[5356] 11/27/07 14:11:26 System Version: 5.2 Build 3790 Service Pack 1
[5188] 11/27/07 14:11:26 ESEBCLI2.DLL Version: 6.5.7638.1 Service Pack 2
[5188] 11/27/07 14:11:26 Command line:
[5188] 11/27/07 14:11:26 "C:\Program Files\Legato\nsr\bin\nsrxchsv.exe" -s legato -g exchange -LL -m mailsrv.goct.com -l full -q -W 78 -N MSEXCH:IS MSEXCH:IS
[5744] 11/27/07 14:11:26 ESEBCLI2.DLL Version: 6.5.7638.1 Service Pack 2
[5356] 11/27/07 14:11:26 ESEBCLI2.DLL Version: 6.5.7638.1 Service Pack 2
[5744] 11/27/07 14:11:26 Command line:
[5744] 11/27/07 14:11:26 "C:\Program Files\Legato\nsr\bin\nsrxchsv.exe" -s legato -g exchange -LL -m mailsrv.goct.com -l full -q -W 78 -N MSEXCH:PF MSEXCH:PF
[5356] 11/27/07 14:11:26 Command line:
[5356] 11/27/07 14:11:26 "C:\Program Files\Legato\nsr\bin\nsrxchsv.exe" -s legato -g exchange -LL -m mailsrv.goct.com -l full -q -W 78 -N MSEXCH:MB MSEXCH:MB
[5188] 11/27/07 14:11:27 NetWorker Server Version: NetWorker 7.2.2.Build.422 Network Edition/10
[5188] 11/27/07 14:11:27 Console Code Page: 936; System Default Locale: 2052; Master Flag: 0
[5188] 11/27/07 14:11:27 Options:
[5188] 11/27/07 14:11:27 Server: legato
[5188] 11/27/07 14:11:27 Client: mailsrv.goct.com
[5188] 11/27/07 14:11:27 Save set name: MSEXCH:IS
[5188] 11/27/07 14:11:27 Pool: None
[5188] 11/27/07 14:11:27 Group: exchange
[5188] 11/27/07 14:11:27 Level: full
[5188] 11/27/07 14:11:27 Compress: False
[5188] 11/27/07 14:11:27 Temporary directory: C:\Program Files\Legato\nsr\tmp
[5188] 11/27/07 14:11:27 Operation type: Traditional
[5188] 11/27/07 14:11:27 Performing an Exchange save operation; save level is Full (Legato Backup Level: full).
[5188] 11/27/07 14:11:27 Parsing parameters from the command line...
[5188] 11/27/07 14:11:27 Opening connection to NetWorker Server...
[5356] 11/27/07 14:11:27 NetWorker Server Version: NetWorker 7.2.2.Build.422 Network Edition/10
[5356] 11/27/07 14:11:27 Console Code Page: 936; System Default Locale: 2052; Master Flag: 0
[5356] 11/27/07 14:11:27 Options:
[5356] 11/27/07 14:11:27 Server: legato
[5356] 11/27/07 14:11:27 Client: mailsrv.goct.com
[5356] 11/27/07 14:11:27 Save set name: MSEXCH:MB
[5356] 11/27/07 14:11:27 Pool: None
[5356] 11/27/07 14:11:27 Group: exchange
[5356] 11/27/07 14:11:27 Level: full
[5356] 11/27/07 14:11:27 Compress: False
[5356] 11/27/07 14:11:27 Temporary directory: C:\Program Files\Legato\nsr\tmp
[5356] 11/27/07 14:11:27 Operation type: Traditional
[5356] 11/27/07 14:11:27 Performing an Exchange save operation; save level is Full (Legato Backup Level: full).
[5356] 11/27/07 14:11:27 Parsing parameters from the command line...
[5356] 11/27/07 14:11:27 Opening connection to NetWorker Server...
[5744] 11/27/07 14:11:27 NetWorker Server Version: NetWorker 7.2.2.Build.422 Network Edition/10
[5744] 11/27/07 14:11:27 Console Code Page: 936; System Default Locale: 2052; Master Flag: 0
[5744] 11/27/07 14:11:27 Options:
[5744] 11/27/07 14:11:27 Server: legato
[5744] 11/27/07 14:11:27 Client: mailsrv.goct.com
[5744] 11/27/07 14:11:27 Save set name: MSEXCH:PF
[5744] 11/27/07 14:11:27 Pool: None
[5744] 11/27/07 14:11:27 Group: exchange
[5744] 11/27/07 14:11:27 Level: full
[5744] 11/27/07 14:11:27 Compress: False
[5744] 11/27/07 14:11:27 Temporary directory: C:\Program Files\Legato\nsr\tmp
[5744] 11/27/07 14:11:27 Operation type: Traditional
[5744] 11/27/07 14:11:27 Performing an Exchange save operation; save level is Full (Legato Backup Level: full).
[5744] 11/27/07 14:11:27 Parsing parameters from the command line...
[5744] 11/27/07 14:11:27 Opening connection to NetWorker Server...
[5356] 11/27/07 14:11:28 Started PerfMon update thread (Id: 5908)
[5356] 11/27/07 14:11:28 Performance monitor update thread running
[5188] 11/27/07 14:11:28 Started PerfMon update thread (Id: 4860)
[5188] 11/27/07 14:11:28 Performance monitor update thread running
[5188] 11/27/07 14:11:28 Preparing Microsoft Information Store on server MAILSRV
[5744] 11/27/07 14:11:28 Started PerfMon update thread (Id: 1160)
[5744] 11/27/07 14:11:28 Performance monitor update thread running
[5744] 11/27/07 14:11:28 Public folders that are not replicated to MAILSRV will not be backed up.
[5744] 11/27/07 14:11:28 Checking for marked public folder tree items
[5744] 11/27/07 14:11:28 Found all marked public folder tree items.
[5744] 11/27/07 14:11:28 Starting backup of folder tree: "Public Folders"
[5356] 11/27/07 14:11:28 Opening connection to Exchange Server...
[5188] 11/27/07 14:11:28 Processing storage group "第一个存储组"
[5188] 11/27/07 14:11:28 apexsv(451): Power Snap module is not installed; traditional operations continuing.
[5188] 11/27/07 14:11:28 Backup storage group 第一个存储组 to legato
[5188] 11/27/07 14:11:28 Save set name: MSEXCH:IS
[5188] 11/27/07 14:11:28 Backup database: 公用文件夹存储(MAILSRV) {10864472-A9F6-4591-8D6B-771AFEBC93CF}
[5188] 11/27/07 14:11:28 Checking size of database "第一个存储组/公用文件夹存储(MAILSRV)"
[5188] 11/27/07 14:11:28 Database "第一个存储组/公用文件夹存储(MAILSRV)" Size: 25 MB
[5356] 11/27/07 14:11:28 mapi(1076): OpenMsgStore() = 0x8004011d: 试图登录到 Microsoft Exchange Server 计算机失败。 (Microsoft Exchange Server 信獯洢)
[5356] 11/27/07 14:11:28 svmain(1105): process_mb_item_backup failed with status = 0x8004011d
[5356] 11/27/07 14:11:29 mapi(1076): OpenMsgStore() = 0x8004011d: 您没有登录权限。 (Microsoft Exchange Server 信獯洢)
[5356] 11/27/07 14:11:29 svmain(1140): end_mb_item_backup failed with status = 0x8004011d
[5356] 11/27/07 14:11:29 Stopping performance monitor update thread.
[5744] 11/27/07 14:11:29 Starting backup of folder: "Internet Newsgroups"
[5356] 11/27/07 14:11:29 Performance monitor update thread terminating
[5356] 11/27/07 14:11:29 Backup operation finished with errors. No savetime was sent.
[5356] 11/27/07 14:11:29 Completion time Tue Nov 27 14:11:29 2007

[5428] 11/27/07 14:11:29 Start time Tue Nov 27 14:11:29 2007
[5428] 11/27/07 14:11:29 Computer Name: MAILSRV User Name: GOCT\administrator (administrator)
[5428] 11/27/07 14:11:29 nsrxchsv_ese.exe Version: 4.1.0.148 Supporting Exchange 2000 and Exchange 2003
[5428] 11/27/07 14:11:29 System Version: 5.2 Build 3790 Service Pack 1
[5428] 11/27/07 14:11:29 ESEBCLI2.DLL Version: 6.5.7638.1 Service Pack 2
[5428] 11/27/07 14:11:29 Command line:
[5428] 11/27/07 14:11:29 "C:\Program Files\Legato\nsr\bin\nsrxchsv.exe" -s legato -g exchange -LL -m mailsrv.goct.com -l full -q -W 78 -N MSEXCH:MB MSEXCH:MB
[5428] 11/27/07 14:11:29 NetWorker Server Version: NetWorker 7.2.2.Build.422 Network Edition/10
[5428] 11/27/07 14:11:29 Console Code Page: 936; System Default Locale: 2052; Master Flag: 0
[5428] 11/27/07 14:11:29 Options:
[5428] 11/27/07 14:11:29 Server: legato
[5428] 11/27/07 14:11:29 Client: mailsrv.goct.com
[5428] 11/27/07 14:11:29 Save set name: MSEXCH:MB
[5428] 11/27/07 14:11:29 Pool: None
[5428] 11/27/07 14:11:29 Group: exchange
[5428] 11/27/07 14:11:29 Level: full
[5428] 11/27/07 14:11:29 Compress: False
[5428] 11/27/07 14:11:29 Temporary directory: C:\Program Files\Legato\nsr\tmp
[5428] 11/27/07 14:11:29 Operation type: Traditional
[5428] 11/27/07 14:11:29 Performing an Exchange save operation; save level is Full (Legato Backup Level: full).
[5428] 11/27/07 14:11:29 Parsing parameters from the command line...
[5428] 11/27/07 14:11:29 Opening connection to NetWorker Server...
[5428] 11/27/07 14:11:29 Started PerfMon update thread (Id: 1392)
[5428] 11/27/07 14:11:29 Performance monitor update thread running
[5428] 11/27/07 14:11:29 Opening connection to Exchange Server...
[5428] 11/27/07 14:11:29 mapi(1076): OpenMsgStore() = 0x8004011d: 试图登录到 Microsoft Exchange Server 计算机失败。 (Microsoft Exchange Server 信獯洢)
[5428] 11/27/07 14:11:29 svmain(1105): process_mb_item_backup failed with status = 0x8004011d
[5428] 11/27/07 14:11:29 mapi(1076): OpenMsgStore() = 0x8004011d: 您没有登录权限。 (Microsoft Exchange Server 信獯洢)
[5428] 11/27/07 14:11:29 svmain(1140): end_mb_item_backup failed with status = 0x8004011d
[5428] 11/27/07 14:11:29 Stopping performance monitor update thread.
[5428] 11/27/07 14:11:30 Performance monitor update thread terminating
[5428] 11/27/07 14:11:30 Backup operation finished with errors. No savetime was sent.
[5428] 11/27/07 14:11:30 Completion time Tue Nov 27 14:11:30 2007
[5744] 11/27/07 14:12:19 /Public Folder Trees/Public Folders/Internet Newsgroups/ 0 KB 0 bytes/sec
[5188] 11/27/07 14:12:20 D:\Program Files\Exchsrvr\mdbdata\pub1.edb 21 MB 21706782 bytes/sec
[5188] 11/27/07 14:12:20 D:\Program Files\Exchsrvr\mdbdata\pub1.stm 4104 KB 24433116 bytes/sec
[5188] 11/27/07 14:12:20 Backup of 公用文件夹存储(MAILSRV) was successful
[5188] 11/27/07 14:12:20 Backup database: 邮箱存储(MAILSRV) {B8800878-A34A-4749-AC58-5A3DCF750696}
[5188] 11/27/07 14:12:20 Checking size of database "第一个存储组/邮箱存储(MAILSRV)"
[5188] 11/27/07 14:12:20 Database "第一个存储组/邮箱存储(MAILSRV)" Size: 8143 MB
[5744] 11/27/07 14:12:21 The backup of Microsoft Exchange Public Folders completed
[5744] 11/27/07 14:12:21 Processed 0 items 0 KB in 0:00:53 0 bytes/second
[5744] 11/27/07 14:12:21 mailsrv.goct.com: MSEXCH:PF 0 KB 00:00:53 0 file(s)
[5744] 11/27/07 14:12:21 Stopping performance monitor update thread.
[5744] 11/27/07 14:12:22 Performance monitor update thread terminating
[5744] 11/27/07 14:12:22 Sent savetime 1196143942 to savegrp.
[5744] 11/27/07 14:12:22 Completion time Tue Nov 27 14:12:22 2007
[5188] 11/27/07 14:12:57 D:\Program Files\Exchsrvr\mdbdata\priv1.edb 1033 MB 28669891 bytes/sec
[5188] 11/27/07 14:17:00 D:\Program Files\Exchsrvr\mdbdata\priv1.stm 7110 MB 29993162 bytes/sec
[5188] 11/27/07 14:17:00 Backup of 邮箱存储(MAILSRV) was successful
[5188] 11/27/07 14:17:00 D:\Program Files\Exchsrvr\mdbdata\E000224F.log 5120 KB 23940091 bytes/sec
[5188] 11/27/07 14:17:00 Backup of logs for storage group 第一个存储组 was successful
[5188] 11/27/07 14:17:03 Processed 5 items 8174 MB in 0:05:35 24987727 bytes/second
[5188] 11/27/07 14:17:03 The backup of 第一个存储组 completed successfully; backup level is Full (Legato Backup Level: full).
[5188] 11/27/07 14:17:03 Completed backup of 第一个存储组 Status: 0x00000000
操作成功完成。
[5188] 11/27/07 14:17:03 The backup of Information Store on MAILSRV completed successfully.
[5188] 11/27/07 14:17:03 mailsrv.goct.com: MSEXCH:IS 8174 MB 00:05:35 5 file(s)
[5188] 11/27/07 14:17:03 Stopping performance monitor update thread.
[5188] 11/27/07 14:17:03 Performance monitor update thread terminating
[5188] 11/27/07 14:17:03 Sent savetime 1196144223 to savegrp.
[5188] 11/27/07 14:17:03 Completion time Tue Nov 27 14:17:03 2007

If your backup account is member of Domain Admins Groups, then he will have deny permissions on Send As Receive As because Domain Admins have explicit deny permissions.

Create an account which is Exchange Administrator, but not member of domain admins