The easiest fix is to restart the MS Exchange VSS writers on the exchange server svmmit427 and then restart the AppSync Service plan.

RDP into the exchange server, open a command prompt in administrator mode to look for the vss writers in "Error" State

Use the command  vssadmin list writers this will list the VSS writers and tell you if they are in an error state or not. (The error message you have cited above is a result of the Microsoft Exchange Replica Writer being in an error state)

Open the services console from (Start > Run > services.msc)

Look for Microsoft Exchange Replication Service , right click and stop the service.

Look for Microsoft Software Shadow Copy Provider service, right click and stop the service.

Ensure that both the above services are not running.

Right click Microsoft Software Shadow Copy Provider and start the service

Right click Microsoft Exchange Replication and start the service.

You can go ahead and restart the App Sync service plan, it should work fine.

With AppSync 3.0.1, you have the ability to perform VSS retry, configurable within the service plan, which generally helps with this situation.

Under Service Plan > application type (SQL or Exchange) > Settings > Create local copy > Advanced Settings