Peamp out of guitar,

You can get these on ebay for not too much money-
Takamine TP 4T Series Acoustic Guitar preamp NEW
Takamine TP 4TD Series Acoustic Guitar preamp NEW Latest Revision

go to Support Yamaha United States Contact and tell them your model and serial probably and they can get you the right preamp. Good luck APX Series Acoustic Electrics Guitars Guitars Basses Musical Instruments...

It does sound to be fried but, you really don't have to replace it with the same exact model, look for an upgrade, I'm sure that manufacture and many others have one better. If it were my guitar, I would definitely think of it as upgrade time. The pickup is probably ok knowing that it can handle heat better due to its location and materials.

looks like broken wiring from pickup to preamp - maybe on jack?

i dont' see where this model has active pickups (guessing this is what you mean by pre-ampped).
The issue can be in a few places.

1) the strings could be too far from the pickups and the instrument needs to be tuned.
2) the pickups are bad
3) your jack is bad
4) the cable is bad
5) your equilizers are not corrected
6) your volume control is turned down or damaged
7) your amp is damaged

this is a small list of the basic possibilities.

If the preamp is in the guitar, the battery is likely dead. When a dead battery "rests" for a short while it recovers a bit and may operate for a short time and shut down.

It is possible the pedal is DESIGNED to be used with an amplified (preamp within guitar) and yours MAY be a passive guitar. You did not tell us what guitar you have.
Many of the processors for guitars depend on having a "line level" signal and that requires that your guitar has a built in preamp.
If your guitar doesn't have a preamp in it, buy a preamp to put ahead of this pedal.

It sounds like the guitar level input to the unit is too low.

NOTE: With this product you MUST use an amplified or electric guitar that has a preamp within it.

If you have a straight guitar that does not have an amp in it, buy a preamp to first run the guitar through.

I want you to do a test. while using the amp plug a pair of headphones into the preamp out... note you will only hear stuff on one side if they are stereo phones and the sound may be fairly weak... while the unit is operating correctely then unplug phones and use it. When it fades out plug in phones compare the level when it was OK... If the preamp output fades lower as well, then we know problem is in the preamp section...

We can do a lot of troubleshooting without opening the amp.

I see nothing in the scheamtics that should be an issue causing this...

Since it didn't fail for the tech, think "what was different?". Are you connecting something else? Foot pedal? Temperature? :Loudness of playing?

Now what else is in common to these two units... AHA! The guitar...

If your guitar has a battery in it, the 20 to 30 minutes fading would correspond to a battery failing and then recovering after you unplug the guitar for a while.

Well if you want goo dpinch harmonics to squeal you need a decent amount of gain and good pickups. What guitar are you using, some lower model passive pickups have bad frequency response when you try to do pinch harmonics. If you have decent pickups I would say get a higher gain preamp and just run the amp on the clean channel. There a re tube preamp pedals out there that have masaive amounts of gain and they are reasonably priced. There are also so good amps out there for a decent price like the 6550 from peavey. I have a 5150 block letter and that thing can produce good pinch harmonics along with my EMGs. Good luck man, oh and there is nothing wrong with your amp, it is just time to move on. There is only so much you can do with solid state amplifiers in my opinion.