First question in ANY lost reverb: bad drive or bad recovery?
Recovery is easy to check... put your finger on the reverb return, it should hum LOUD.
Drive can be checked by substituting a speaker or headphones for the reverb tank input. In classic Fender a 4-8 ohm speaker is perfect. Dummy-load the main output so you can hear the plink in the reverb driver and test speaker.
In this case we don't know the reverb tank impedance, and we might suspect it isn't 4-8 ohms. You could meter the tank and see if it is a few ohms, a hundred ohms, or many hundred ohms.
There's test-point voltages on page 1.
Did you check the DC voltages? Which ones go way-wrong after 20 seconds?
In general I would not suspect a tank... tanks don't heat up. (Except this one does.) Likewise the chip "usually" will work or dont-work. Bad solder joint is always possible, but some poking should provoke it to cut in and out, and you know that dance.
I figured-out some of the "right" voltages. Not same-as the test-point numbers, but it is a funky plan and some variation is expected.
I said tanks don't heat. This driver runs _DC_ through the tank. That's barely kosher. The tank coil _will_ get warm. So it very well could be a broken lead inside the winding, which touches when cold but opens when the coil expands.
This driver is hyper-fussy about tank input DC resistance. I figure it needs to be 100 ohms. A few-ohm or 1K winding will throw the power transistor out of bounds, no signal.
If the tank "may" be burned-open, replace it with 100 ohms and see if the DC voltages now hold near nominal.