One Panasonic RQ S15 that I repaired forget's tape is inside and won't play. It goes like this: I put tape in, play it, it plays one song or songs on both sides with autoreverse. Then when I leave it for some time (could be 5 minutes, could be hours) and when I come back and push play it shows light operate but after a second it just stops. Funny is that it has no problem with rewind or fast forward tape. Only way I can continue playing is opening door with casette at least that it goes out and doesn't contact tape selector. Then I close the door and Panasonic 'resets' operation and I can again play it. I have seen situatios when tape selector doesn't work at all, but this is strange. And I'm not sure it's tape selector problem. Maybe it goes to sleep state? I don't have operation manual for it, only service manual.
By "tape selector" I suppose you mean the tape in switch, which detects a cassette is inserted, no ? I would clean that first (Kontakt 60), just to eliminate it as a potential cause. If the problem is still there, at least you know for sure that's not the cause. Spray some cleaner into it and push it about 20-30 times to be very sure the cleaner has done its job.