I have the excact same problem, my setup is:
Windows sbs 2003 server, with exchange and a smtp connector relaying mail to remote host. when avast has been running for some days, it will eventually begin to drop connections to the virtual smtp server, saying: conenction limit in avast has been reached.
a restart of avast services seems to fix the problem until the service has run for a couple of more days.
I'm using Avast server edition for sbs servers. With network shield, exchange scanner and internet mail / pop3 scanner running, all without errors, and they do find virus, so they work ;o).
This problem is rather serious, as it is not only remote mailsending that is beeing halted, when smtp service is hindered in functioning, it will not route mail internally in the exchange server, hence all communication in the company stops.
And help, thoughts and ideas are greatly appreciated. ;o)