In our case, System Event Log Warnings 386 and 434 from source CPQTeamMP alternated. We could not RDP into the server. One NIC intermittently appeared as disconnected in the HP Network Config Utility. The following solution assumes you have teamed the NICS (by highlighting both and clicking Team -> OK).
Start the HP Network Configuration Utility -> Highlight the top "HP Network Team" entry -> Go to Properties. Under "Team Type Selection", change from "Automatic" to "Switch Assisted Load Balancing with Fault Tolerance".
I am not a Cisco wizard, but I assume there was a conflict between the NIC Team software and the Cisco switch, as to which was responsible for sharing the load between ports/NICs. This appears to have resolved the issue.