I can’t recall that I have ever experienced GM burnout. I’ve been GMing continuously since November of 1992, and for nearly all of that time, I’ve been running two or three campaigns in parallel. (I was down to one after we moved out of San Diego, but now I have a group up here in Riverside.) For that matter, I’ve never experienced writer’s block, and I’m somewhere past twenty books for SJ Games.
This may be simply that I have a naturally happy disposition (as far as I can tell I’m nearly immune to self-esteem issues). I hesitate to attribute it to my unusual approach to setting up games, because I don’t want to claim that that would work for other GMs.
However, what I did for many years was to come up with a list of from half a dozen to fifty ideas for campaigns I might run; hand it around to a dozen or so possible players; and try to select two or three campaigns that players gave high ratings to, and that together left no player out in the cold, and that produced groups who could play together. Over nearly that whole span, I brought in a new player or two with every new cycle. The usual duration was two years, but once I extended all three (very well liked) campaigns to three years; I’ve run a couple of cycles of mini campaigns lasting six months (handy for testing out weirder ideas); and my current surviving San Diego campaign (actually meeting in Poway, a suburb) is in its fifth year, though since I’ve moved to Riverside I don’t run it every month.
I run more GURPS than anything else, but I’ve run a whole lot of systems, and in fact my favorite way to figure out a new system is to try running a campaign in it. On the other hand, this has uncovered some really bad systems; I will never again try to run Space 1889 (though I loved the worldbuilding!), In Nomine, or Godlike, for example.
I consider myself mostly fortunate in my players, particularly the San Diego circle; most of them are quite seriously involved in roleplaying, and have excellent firewalling abilities. Perhaps this partly reflects my having players who were recommended by other players, iteratively, so I’ve gotten people who fit together well. On the other hand, I’ve had one player voted off the island by nearly everyone refusing to play in a campaign that involved him, and another who went a fair part of the way to that same position.