A Who question

[Psychotic]

I raided Wikipedia!

It is not known how long a Time Lord can live, although the Doctor claimed in The War Games that Time Lords could live forever, "barring accidents."

As for regenerations, The Master gained additional regenerations by possessing another person's body, although the Doctor is unlikely to do that, as he isn't evil.

It may be that the Time Lords have the ability to circumvent the limit — in The Five Doctors the Master is offered a new cycle of regenerations by the High Council in exchange for his help.

And here's one about the Valeyard (another Time Lord, and possibly a future regeneration for the Doctor himself)

To prevent the Doctor discovering the secret and revealing it, they used the Valeyard to try to have the Doctor executed under the pretence of a trial. The reward for the Valeyard's actions would have been to give him all of the Doctor's remaining regenerations and make his existence concrete.

So there's no doubt The Doctor will be given additional regenerations instead of being allowed to die once and for all.