The Ambassadors of Death (Pertwee) and Survival (McCoy). The Pertwee ep was significantly better than the McCoy show and leaves little doubt that the franchise was ready for a rest by '89.
Not the franchise, just John Nathan-Turner. My recollection of the opinion expressed in fanzines and such at the time (which I agreed with) was that JNT, the show's longest-running producer by a wide margin, had stayed in the chair too long and it was time to let someone else come in and bring a fresh voice and approach to the show, just like each new Doctor brought a new energy and personality to the show.
People like to use "franchise fatigue" as an excuse for a series losing viewers, but it's nonsense. People were saying in 2005 that Star Trek was so "fatigued" that it would need to take a couple of decades off before the audience was "ready" for it to return. And I think I heard people say in 2014 that the Spider-Man movies were fatigued and needed to take a decade or so off. "Franchise fatigue" is just code for "The recent stuff just isn't that good but we want to blame its failure on the audience instead." All it takes is a fresh new approach and any "fatigue" vanishes and the audience returns -- or else a whole new audience is drawn in and takes the place of the old one.