As jr tech mentions
The cap on the AVC line may be leaky and interfering with the automatic gain function. Just change one wax cap at a time, so you don't forget where its replacement connects to. Change the electrolytic caps too.
Thought comes to mind: check that the antenna circuit doesn't have a broken wire. Though I'd think that the 12BE6 grid would not be biased properly and the set would be deaf.
Though it's way down on my list of suspects today, a weak IF tube or 12BE6 could be the problem. But I always blame wax caps first, just replace them on sight.