From my experience, I could go on with my role for a several months without burning out or running out of new ideas for rp, but lately I realized that at the duration of one year I completely burned out and I lost all passion for my role and Gor in general.
The main reason for this sort of burning out, specially to my role which was people oriented and a very intense one was that my character did not evolve. This is mostly a sim limitation, some sims would not have room for a plot to evolve the character beyond their actual status. For instance, if a sim has an Ubar, it's likely to stay this way for as long as the Ubar wishes to remain. But if that same sim had a coup plot cooking, and an attempt. Lots of characters will face a sever change in their path. Either they'd evolve and rise to power or devolve and escape to become outlaws or get killed if caught. Dramatic changes that are out taken by roleplayers is something that has been missing from most sims that I have seen. A panther En would ever be the En, unchallenged. Same thing.
This is the scenario that happened to me, the role became an errand and my plot became a routine my story repeated itself day by day with the few differences of the additions and innovations I made. Those creative additions to my roleplay did not push my role anywhere new, it simply supplied the narrow circles that I had to abide to.
Second reason for burnout is "rp-leeching", being in a central character for a while is no problem for me, but finding that some roleplayers would depend on me for their own roleplay is consuming. Meaning that sometimes you'd find that other roleplayers would come to you with absolutely nothing to offer in rp but a "Tal" and a little comment about the weather and they stick around you so as to get into an intriguing discussion or an uprising conflict. For instance if you're a slaver training your slave, you'd find someone hopping in your kennel adding up instructions to your training slave. And mostly because such roleplayers lack creative ideas they tend to give the wrong instructions. I found that those characters drained me most, their rp is a demand not an addition to the scene and their contributions require a lot of fixing later on.
Bottom line, A role with potential to evolve or devolve, in a sim that allows that is one good factor to escape burning out. A community of roleplayers that do not depend on the central roles to the limit of wearing them down reduces the chances of those rpers loosing their interest or their enjoyment.
.. The Reader
If you don't understand what you read, don't embarrass yourself.