Question : Problem: Citrix Farm dropping connections

I have a Citrix farm that started dropping connections.  The only thing that changed where the updates that Microsoft put out on the 13th.  Is there a way to troubleshoot dropped connections?

Answer : Problem: Citrix Farm dropping connections

You said NICs, like plural?  Why are you multi-homing a server that takes about 50k of bandwidth per user?  One 1Gbps link is all you should need.  Fault tolerance happens naturally when you have many servers in your farm.  I never recommend teaming; you chew up more switchports and introduce easy ways to have networking problems.  This is not a SQL server...even then...clustering is better HA IMO...anyway, that might not even be what's going on.  
If you do have more than one NIC in use on the same subnet then I bet you Spanning Tree is putting you into a blocking state.  That would explain the up and down.