For what it's worth, I have 2 A60s and they have both displayed similar faults at some stage in their lives.
In both case it turned out to be the horrible volume pot. They wear and then a length of the resistive carbon track falls off and shorts the pot out. I assume that this then results in the output stage seeing an input level it was never intended to deal with.
As the pot's are rubbish anyway, you could do worse than replace yours, as it's probably overdue even if it doesn't cure the fault in your case it eliminates a common cause of problems on the A60.
It's not a difficult job, just a bit time consuming as you have to detach the PCB from the metal base which is pretty much a complete stripdown.
Maplin now seem to be the only people supplying them, but they are cheap, which is good as they are very out of balance at the bottom of their range.
That is fixable to some extent:

"While converting the master volume in a friend's Twin Reverb to post-pi,
here's how I balanced an Alpha 250k dual-ganged pot. You can only get to the
inside of the rear pot, unless you want to figure out a way to destroy the
crimp on the end of the shaft and glue it all back together afterwards. So,
I just worked on the back pot.

I started at the full ccw position. I turned it cw in little increments and
checked the resistance from bottom to wiper on both pots until I found a
spot where the difference was 1k. I went by 1k because that was the lowest
amount I could read on the VOM - if I were using a lower-valued pot and
reading the resistance on a lower scale, then I'd look for a smaller
difference. Anyway, if the back pot had more resistance than the front one,
I would take a pencil and put some graphite down at the outer edge of the
conductive element until they were the same. If the back pot had less
resistance than the front pot, then I would scrape at the edge of the
conductive element with a penknife or one of the test probes. It takes just
the tiniest perceptable scratch to increase the resistance 1k. I kept going
in steps all the way up to full cw. The pot is now balanced within 1k.

I was careful to make all the additions and removals outside the path of the
wiper. The conductive element was a little bit wider than the path of the
wiper all the way around.

Will the pot stay balanced over the long run? I don't know, but it's plainly
better than stock now. If wear and tear is going to unbalance it, it still
won't be any worse than a stock pot with the same wear and tear."