We are seeing a similar problem except it is intermittent that the server has problems. What we see is a very slow connection. A check of the Cisco server shows lots of errors on the connection. We have found that every time we can fix this without a reboot by doing anything that breaks the connection to the server. Either by physically pulling the network cable, or by disabling and enabling the Cisco port or taking the server port to disable / enable. Our ports are configured for 100 / Full on the server and on the Cisco switch. It seems like the NIC is negotiating a connection at 100 / Half during boot up and then Windows Server 2003 accepts that the connection is OK even though the setting is fixed at 100 / Full. It is only after Windows sees a connection loss that it applies the 100 / Full that we've put in the configuration.
We are looking for a way for make the NIC card come up in 100 / Full. But for now we can fix it by breaking the connection and restoring it.