We've got a very small ASP.NET 2.0 website running on a server (Win 2k3 + latest SP) which is virtualised via VMWare (Infrastructure).
At random times (ie - not the same day of the week/ month/ etc) all traffic to the server stops as the network card stops responding.
We've found the only way to solve the problem is to reboot the server.
Nothing appears in Event Viewer which could indicate that there was a failure in something so I can't even think of where to start trying to diagnose the problem.
The site has been hosted on two separate VM's and the problem has occurred on both of them. The site runs SSL and it has a very small amount of .NET code which does some database interaction. It also has very small amounts of traffic so it's not falling over due to strain.
I've had the same problem on Vmware ESXi 3.5.0 and ended up running a small service that pings the default gateway from within the virtual machine every 120 seconds and the problem never reappeared. Once I migrated to Vmware ESXi 4.0.0 the problem went away.
I have experienced something similar. If you are using Netbios names in your application you may experience this... Can you change any references to fully qualified domains?