Well avast doesn't delete anything autonomously it scans and alerts to infection and presumably that isn't the case ?
There is no built in functionality to remove restore points other than infected restore points.
Depending on the version of avast you have 5.x or 6.0 then you have automated actions upon detecting an infected item, by default that is move to the chest, so unless you have changed the default settings it shouldn't automatically delete.
I have avast 6.0.1000 on my win7 starter, Netbook and that has system restore enabled and I haven't seen what you are experiencing. For me I have always considered system restore as flaky (certainly not 100%) and have always disabled it and user Drive Imaging software as a replacement for system restore.
Now avast does create restore points usually before a program update, etc. so depending on your system restore settings and size allocated to system restore, it is possible that the oldest restore points may be dropped.