yeah my computer runs almost all day (max...a week non stop, without reboot) but my DSL disconnects every 1,5 days (dynamic IP)
No problems with Avast! so far,...not even concerning memory things
I do have 640 MB off SDram
computer => pIII, 600 Mhz - W2K Pro SP4 (pretty old,... :p)
I do not see why you should disable Avast!,...it hardly uses RAM memory (that is one of the main-things I like this software)