I was under the impression that The Master was at the end of his regeneration cycle around The Keeper of Traken. And Romana proved that some Timelords can control their regeneration. The role only really needed to be recast once, for tragic reasons.

More meta, think about the real reason The Doctor regenerated. I wonder how much longer Pertwee would've held on to the role had he not lost his friend, Roger Delgado; I've heard that that was a factor in his decision to leave the show.