Same thing is happening to me. Avast will randomly turn off its background service. I tell it to turn it back on, it does, and then a few minutes later its off again. This is on version 12.3.2280 but it also did it on 12.3.2279. I'm pretty sure it only started today.
Checked to make sure that the self-protection was turned on - it was. Did a repair of avast and it didn't help.