Vlk,
It turns out that the backup problem had nothing to do with Avast! Instead, it was caused by SQL Server, a problem that I have now resolved.
By the way, I'm now one week into my trial of Avast! and I am very favorably impressed. It's so nice to have a comprehensive anti-virus package for Small Business Server that works so well right out of the box.
Thanks for your help and for the excellent software!
Ken