I may be talking through my hat, and I am just going by memory, but I had the impression that the limit on regenerations was arbitrarily placed on Time Lords by their own bureaucracy believing that immortality was corrupting. I believe Rassilon, Omega and (in some stories) the Other were immortal. Omega still lives as anti-matter. Rassilon, though he developed the “modern” Galifreyan society, became quite the dictator and was entombed alive (or in a state capable of regenerating) in a prison/monument by his own people. (His tyranny was hinted at but never made clear in the show, thus is not cannon. He apparently agrees that immortality is corrupting by the time of the Five Doctors, as has been pointed out). As against this theory, the TV show suggests that Rassilon may not have been immortal, but likely discovered the secret of immortality.
It appears that it has always been possible for the Time Lords to grant further regenerations. In any event, the TV show does have examples which would suggest this is the case. As has already been mentioned, the Master has been given further regenerations on more than one occasion.
When Sylvester McCoy was the Doctor, there was a discussion of having him be the Other, and some clues were dropped into the early stories (ie “I am MORE than just another Time Lord”) but the show was cancelled and thus the intention is not cannon. Some books (of questionable cannon) suggest the Doctor is “the Other” and if he is, he would not be subject to the same regeneration restrictions, of course. If he is the Other, it might explain the rather confusing sequence of previous “lives” from Tom Baker’s “The Brain of Morbius” which suggests the Doctor has already surpassed the usual 12 regenerations. (Such fun we fans have in coming up with rational (or rational-like) explanations for what is really a continuity error.)
Again, going from memory, and for those who only watch NuWho, the Other (not cannon as not actually introduced into the TV show) was one of three Time Lords who built the society as it is known currently. (It was once a matriarchal society with one immortal female leader) The three, Rassilon, Omega, and the Other, overthrew the previous regime and made possible time travel by harnessing the power of a black hole known as the Eye of Harmony. Omega, the scientist, was assumed killed in harnessing the Eye, but was actually turned into anti-matter and soon became paranoid and embittered. Rassilon, the soldier and political leader, guided his people for many years slowly becoming more and more tyrannical and power hungry until he too was overthrown. The Other, unable to stop Rassilon’s power grab, became disillusioned and threw himself into machine which was used to produce little Time Lords, saying that he would return. His genetic material was assumed spread throughout the machine and reused. The belief was that he would be able to somehow return again as the Other.
I think the writers of the show have a few very easy ways of going past the 12 regen limit without blasting holes in continuity. I can hardly wait to see which is chosen.