The Master tried to regenerate a 13th time (into a 14th incarnation) and overcome death through various medical means, but it didn't work, leaving him a withered husk during the Tom Baker years. He eventually perfected a mind-transference device and took over the body of Tremas, a humanoid alien from the planet Traken (and the father of the Doctor's companion Nyssa). It's in this form that he appeared throughout the time of the Fifth, Sixth and Seventh Doctors.

In THE FIVE DOCTORS the High Council offered the Master a new set of regenerations. Fans have taken this to mean that the Master's new, non-Time Lord body could be given a set of regenerations (and possibly anyone could), but the Time Lords themselves can't simply keep giving themselves more and more regenerations. If they could, the Master and Borusa (another Time Lord seeking to avoid death) would simply have found a way of stealing this process rather than the insanely dangerous and elaborate plans they did set in motion.

The general assessment is that the Doctor's impending 'death' could make for an excellent season-spanning storyline, presumably ending in the Doctor finding a way of circumventing it. The BBC certainly won't simply stop the series because of a quasi-obscure story point from 35 years ago.