I encountered a problem on both the Kenwood TS-820 and the R-820, when using either of them for transmission. In both cases the solution was similar.
After a transmission, there was no immediate reception from the set. The S-meter hang in the RH corner. After some time, varying from half a second (in the beginning) to several seconds (later in time), reception was back.
Ticking on the main relay (RL-3 with decks RL-11, -12, -13 and -14 on the relay unit X43-1190-00) brought reception back immediately, but in the end this no longer worked. I was lucky to have a spare (OMRON) relay, and I replaced it: the whole problem was over.
As stated, a similar situation occurred for the R-820, and also here replacing the relay solved it.
I was greatful to the previous owner of the set (heritage, thanks OM Nick) that he had these spare relays.
Later I heard the cause of the relay problem: Philips, the famous one in Eindhoven, Holland, used similar relays in their early video recorders. Their Electronic Lab found out (after troubleshooting and testing) that over time the weakeners in the plastic cover of the relay evaporate from the plastic material, and more or less coat the switching contacts in the relay. Therefore I asume that cleaning the contacts with a small piece of thin yet strong paper with some cleaning spray, may solve your problem as well.
I myselve did not try that yet (I wait for another 15 years before these spare relays trouble me: then I'll be retired, and I will have more time for that!
Good luck, I hope it solves your Rx problem as well.