This answer poses the possibility of an emergency that would require Apollo astronauts to spend the rest of the mission in their suits:
A hole in the CSM might be more of an issue, since large portions of the pressure vessel are inaccessible during flight. If such an inacessible hole happened, it's likely the crew would have gone to suits, on umbilicals, and taken the very next opportunity to aim for Earth.
At what phase of the mission would such an emergency occur that would maximize the amount of time that the Apollo astronauts would need to spend in their suits?
There briefly was an answer (deleted by its own author) about how running out of supplies would be a limiting factor. True, but that's not how I've asked to approach the question ("what phase of the mission..."). Therefore, I've added the trajectory tag.
I had previously said that "Whatever Apollo 13 did" is not a satisfactory answer. My chief concern is that an acceptable answer is backed up by some sort of analysis, and not just idle speculation. You can do the calculations yourself (as in PearsonArtPhoto's answer), or you can cite NASA documentation, just as long as someone has run the numbers. However, if you're going to use a quote from Jim Lovell or Gene Kranz, then you ought to show that they were citing actual analysis rather than making a (very) educated guess.
Will the Apollo 13 scenario end up being the answer? My gut-level feeling is that it will be very close to the worst case, but that there still is an even longer scenario.