JFET - Ceramic Resonator - Oscillator Phenomonom going in and out of oscillation
Hmm, I have too little reputation to leave a comment.  I wonder if I can leave an answer.

I agree it must be thermal, but which component?  You can put a heat source on or near each one, to try to reproduce the fade.  Or, once it has faded, you can used "canned air" to cool off each component to see if it comes back to life.  To do this you need to turn the can upside down so it sprays Freon. The evaporation rapidly cools things.

Based on the behavior, my guess would be that the transistor is heating, and its cutoff voltage somehow creeping toward 0.  This is hard to reconcile with the low power levels you describe, however.  The other temperature effect that could result in stability would be a change in gain, but then I don't think the drain current would go to zero.

Cool problem, looking forward to the resolution!