I've been assuming it takes that long for the caps to recondition (or whatever the term is). Is there a way to measure if the caps are in spec?'Form up' is the technical phrase, and yes. They would have to be measured when cold and discharged to see how much current they need to charge up and what value they actually are. This does sound like a cap failure though.
I'm working on an amp right now that won't even play when you first turn it on- after about 30 seconds you can hear distortion, and after about two minutes its sounding about right. Both channels- so it can only be the power supply. I suspect a cap and probably the resistor the feeds it as well.
But one thing about trouble-shooting: never make assumptions!