The reason I mentioned another AV is that most new systems come with one pre installed ?
Another thought is that in Win8.1 windows defender is effectively a full AV (Microsoft Security Essentials), this however, should be disabled by the OS when you install a third party AV like avast. You could check and ensure windows defender is in fact disabled.
It is a bit strange that this is only going on on one of the systems though, presumably these are all the same sort of installed applications, etc.
EDIT: if you check in the task manager is avast actually running (avastSvc.exe) and just the avastUI.exe (avast user interface, tray icon) not running ?
Outside of this I'm a little short on other suggestions as I don't use win8.1.