After watching to the end of season 9, I thought of starting back from Eccleston onwards. I got to Last of the Time Lords with the Master and the Utopians, and the Master decides to refuse to regenerate. Now in the penultimate episode of series 9, the Doctor states that when Time Lords are dying, even if they cannot regenerate their body tries to regenerate automatically - they have no choice. So the Master's body should have done it for him whether he wanted to or not. Is this the writers deciding to forget that episode, or is it me just being thick?
The answer to this depends on the Time Lord and their degree of control over regeneration.
There are two instances when a Time Lord refused regeneration, or potentially refusing it as is the second case.
The first being The Master when he willingly died to spite the Doctor in Last of the Time Lords. The second was the Fifth Doctor in an audio episode called The Gathering.
the Fifth Doctor once threatened System with resisting regeneration to stop the device from learning the biological details of the act. (AUDIO: The Gathering)
There have also been scenes where Time Lords resisted fully regenerating as well, such as when the Ninth Doctor explained to Rose what was happening to him or when the Tenth Doctor held off his regeneration.
The Ninth Doctor was able to hold off his impending regeneration for a few moments to explain what was happening to Rose Tyler. (TV: The Parting of the Ways) After subjecting his body to a lethal amount of radiation, the Tenth Doctor was able to delay the regenerative process long enough to revisit each of his former companions of his own incarnation and his past selves as well before he finally regenerated.
Overall as previously stated it depends on their control over their body and regeneration. It can be said that The Doctor and The Master both have pretty high control over it. One being that The Master fully prevented his regeneration.
And the second being that the Tenth Doctor was able to regenerate but keep the same body, essentially using up a regeneration.