I have experienced the same thing but with excessive CPU usage. Using AVG 2011 (server edition) on a SBS2003 R2 box running Exchange 2003 (latest service pack).
After upgrading from AVG9, there were no problems at first. Then I started getting a lot of errors in the event log about exchange virtual memory usage and virtual memory fragmentation. This continued over the next 24 hours until Exchange just stopped sending any emails. After re-booting, the SMTP service and IIS services wouldn't start properly.
I then found out about the iisreset /stop and iisreset /start commands which I ran and successfully got email and intranet back up and running. Then again, another 24 hours later, exactly the same thing.
Normally, our server ticks along at an average 1-3% CPU usage. The disk queue length and pages/sec figures occasionally spike but normally tick along at a very low level. I noticed that with AVG VSAPI plug-in running, all of these figures jumped up way high. CPU was up to around 30%, disk queue and pages/sec were constantly maxed out. Disable the plug-in (wait about a minute for it to stop) and the figures return to normal. I disabled it and rebooted the server on Friday and it's been completely fine over the weekend.
If you download Process Explorer from Microsoft's website, you can see how the VSAPI plug-in affects the store.exe process very clearly.
I also had some hilarious "advice" from AVG (like check whether I had things like LinkScanner enabled which doesn't even exist in the server version). I am still awaiting a sensible reply from someone at AVG who actually has a slight clue what they're talking about (this seems to be quite rare, as I've often been given conflicting advice from different people there, and they seem very quick to blame some other process on your computer).
At the moment, I just have the VSAPI turned off but that's really all we use AVG on the server for so if they don't come up with a fix this week, I'll definitely be getting my money back and going elsewhere.