As long as he can do the job with integrity and competence, and as long as he still wants the job.
Basically, the only way a style should put someone else in as the head, is if something like the following occurs:
1) The grandmaster is mentally incapacitated, such as Alzheimer's disease turning him into a shell of what he once was.
2) The grandmaster no longer cares about the system, and lets it rot. In this case, though, it's more likely that the best people will simply leave the system and start their own faction, etc.
3) The grandmaster pulls a "Count Dante" and does unlawful things that compromise the integrity of the system, such as burning down rival dojos, trying to barge into rival dojos and start some nasty fights, etc.
4) The grandmaster is physically incapacitated to the point that no duties can be carried out, such as being in a coma, or near the point of certain death. If he truly cares about the style, then he will have his successor already named. Even if it's just a temporary appointment, maybe it can help stabilize things.
It should really only be done when something drastic happens, where the very livelihood of the style is in question. Otherwise, for people to attempt a coup would be dishonorable, indeed.