One time I was working on a Crate GX130c guitar amp and it was acting strange. Just as your amp it would turn on okay and then get a weird volume or crackle even then it would start to drop the signal. Eventually it would shut down and turn back on by itself... All this happened within about 2 minutes. This would happen every time you turned on the amp. What I found was a 120 ohm 10 watt wire wound resistor was cooking up so hot that it was getting loose from trace or something. I don't think wire wound resistors typically get intermittent but this was the issue possibly. The wire wound cement was cracking and even though it read around 120 ohm cold it was heating up and loosing the battle, then the amp would shut off. Now these resistors on this amp would heat up anyhow, but after years of use it was toasted. I replaced all the wire wounds on the amp and it stopped that problem. The amp lives on now!
In your case this might not be what is happening exactly, but what is happening (very probable) is that some component is heating up too much. Each time it heats up something is loose inside and at that point the amp becomes unstable. When it starts to break up and act funny does tapping on the amp have any effect to bring the signal back momentarily? A cold solder joint is hard to detect but chopsticks help.
In your case this might not be what is happening exactly, but what is happening (very probable) is that some component is heating up too much. Each time it heats up something is loose inside and at that point the amp becomes unstable. When it starts to break up and act funny does tapping on the amp have any effect to bring the signal back momentarily? A cold solder joint is hard to detect but chopsticks help.