Sony STR AV-19 receiver

I'd try to measure if (one of) the output(s) have a DC offset. Too much DC would prevent the protection circuit from connecting the speakers until the offset drifts within tolerance.

 

It depends on how "adventurous" you are. Obviously a service manual would come in handy, and if you are to do something about it you'll have to open the receiver anyway.
You could start with measuring the DC on the speaker outputs (w/o speakers connected). Of course you won't read anything until the protection ciruit "approves" it, but if there's then a few hundred millivolts - and they gradually go down - you can assume that DC offset is the problem. Maybe only one channel is affected.
Then there is the issue of fixing it. Some amps have an adjustment for it, others are fixed - and then there may be a leaky capacitor or something being the culprit (and for that a diagram is a must).