Sorry to hear about your amp.
Looking at nudies online, the A308 is a true dual mono. That is, both channels are separate pretty much from the power switch onwards.
If both channels are dead when it stops working, then the fault is in the section that’s common to both channels. Which is kind of good news because that section is pretty small.
Your user manual says this:
Press the POWER button on the A308
amplifier - the blue power LED on the front
panel will light indicating that the unit is
ready for use. However, for about five seconds
no sound will be heard from your
speakers, and the red mute LED will light to
confirm initial mute action.
In other words, each time you turn it on the unit checks for DC offset on the speaker outputs. That’s protection mode. If no DC is detected, as is normal, then you should hear a relay clicking as the power LED turns from red to blue. The amp has come out of protection mode and is ready to use.
If you hear no click and the LED stays red, then like Atmasphere said the protection circuitry should be looked at first. Guess that tiny toroidal is what powers it.
For completeness’s sake, an amp that won’t come out of protection either means that there is a downstream fault and the protection circuit is doing its job, or the amp is OK and the fault is in the protection circuit itself.
It’s kind of unusual in your case that the fault is intermittent.
One last thought: the remote has a mute button. It’s a long shot, but just to check that box take the batteries out of the remote and see if that makes any difference.
Good luck!

