Did what you suggested: uninstalled, reinstalled the fresh download.
Hasn't worked. It has, perhaps, decreased the number of times in a day it either shuts down some (or all) of the shields, or is in "an unstable" state, but it's still doing the same thing.
I'm about to jump ship and go back to unnamed product.
[addendum: Who changed the name of the other AV product to "unnamed product"? I don't appreciate that. Surely, if you believe in aVast strongly enough, you can tolerate a competitor's name in the forums. Sheesh, how childish...]