I guess it could be a lot of things. the fact that it does it whan it is warm must be a clue. it could be a bad tube socket connection or bad solder joint. you mentioned that you replaced other parts but have you replaced the filter capacitors? I would at least sub some new ones in as a test. you could also try re-wetting all solder joints to see if that fixes it , sometimes a cold solder joint can cause issues like this and be hard to spot. If the plates of the tuning capacitor had some metal filings in them they could develop an intermittent short that could kill all reception but i don’t think it would be heat related.
when the radio dies does it completely die? or is shtere still some hum? any effect when you tune different stations in this condition? if it is a common set do you have others that you could borrow tubes from as a test?
could the power transformer be working and partly shorted? any unusual heat build up? is it drawing a reasonable ammount of current , like 1 amp and not 3 amps? what kind of radio is it?
you could try poking at various connections etc, with a plastic stick while it is playing , if you are lucky this could uncover the intermittent. I have heard of others also using cold spray for the purpose of troubleshooting things like this. I hope that helps somewhat. perhaps others could also comment with their ideas?