DM Burnout is rough and I've seen it in my group before. Over the year of playing we developed a number of rules and guidelines that has kept our group strong for 12 years.
My group has a core of 4 people. 3 players and one DM. We have found that this works best for us. 3 of us have played together since high school over 10 years ago. One of our original core players finally got booted about 5 years ago for various reasons. One new core player has recently established himself. We are always looking for new players and we have brought in several over the years. None of them have lasted although a couple do pop in as guest players once in a while. But the core group seems to stay at around 4 people. Part of it is our strict policies. But our policies have also helped to insure that we have a good time playing together and we are going on 12 years now.
A few people have been booted over the years and one guy walked out because the DM wouldn't allow his munchkin rules rapist PC (and we generally powergame so for us to call someone a munchkin is pretty serious!)
Anyway, several things that always helped my group:
1) Everyone must purchase and own their own PHB. No PHB, no play. No PDF or SRD file either (see rule 3). You must own the actual WotC published hardbound book.
2) Everyone is expected to read and understand their PHB and must at least understand all the abilities related to their class. If you play a rogue or fighter, you better know what all of your feats and class abilities do without having to look them up. If the DM questions you and you don't know something so basic you should know it, you get docked XP. Likewise Mages are expected to generally know what all their memorized or known spells do without looking them up. Some lookups are fine. But if your initiative turn comes around and you aren't ready to cast your spell you get skipped. If it continues to be a problem, you get booted from the game and then have to pass a D&D knowledge test before you can play again.
3) No distractions. All PCs, PDAs, programmable calcs etc. must be turned off during the game. That includes cellphones. You can have your phone on vibrate but if you ever take a call in the middle of the game, you get docked serious XP and may be booted if it becomes a serious problem. Keep non-related game conversation to a minimum.
4) Be on time and ready to play or you get docked XP.
5) No arguing with the DM during play. You may bring to his attention a mistake he made and at that point the DM will either stop play to have someone look up the rule or will simply keep playing and will asked that the rule be checked up on after the game. Continuing to argue with the DM is XP dock or just an outright boot from the game.
6) Rotate DM duties. My group has one main DM and one backup DM. I'm the backup DM and run a game once every 2 months or so in order to give the main DM a chance to relax and play once in a while.
7) Change campaigns or rule sets. Once in a while we play Mutants and Masterminds or something totally different like Rifts in order to get a change of pace. But we always come back to D&D after a few sessions.
8) Avoid minis like the plague. This one may be controversial since some people like minis. But we found that our enjoyment of the game upped considerably when we banned minis from combat. We still use them just to generally know where our guys are, but we no longer move them around like chess pieces. When 3e first came out and we used a lot of minis we found that combat started to get stale. It was all about moving your mini around, trying triangulate the maximum square spell coverage, rolling dice and shouting hit or miss. We banned minis and went back to using our imaginations to describe combat. Keeping track of character position in our heads, describing our characters movement and action, instead of moving a mini on a grid, etc. Everybody seemed to have a lot more fun and the action was a lot more intense and cinematic. It also forced people to pay attention and kept their mind active and energized. We even had a lot less rule lookups because we were no longer so concerned with precision and more with having a good time and describing a cool scene.
9) Know the rules and they fade into the background. Don't know the rules and they will be a thorn in your side. This seems obvious but its important. When we first started playing 3e three years ago we were always looking things up. Now, through strict policies of requiring rules knowledge (see above

) and lots of 3e experience, we all know the rules so well we rarely look them up anymore. Our books rarely get opened at the table anymore during play. Our games run very smoothly.
10) Share something with your gaming buddies besides the game. Sometimes we all get together to see movie or hang out and play Xbox together just to get away from D&D.
11) Play the game because you really want to play, not just to "hang out". Sometimes we make sure that everyone is really in the mood to play. If they aren't in the mood to play its better that they don't play and bring everyone else down.
12) No game is better than one where you don't have fun. If you force yourself to play and you really aren't having fun then you are really going to get burned out fast. Nothing wrong with taking a break. We'll play your character as an NPC so you won't be penalized for missing a session once in a while if you need a break (as opposed to missing a session because you are being flaky, in which case penalties apply).
13) Always be on the lookout for new players or DMs. New players and DMs can bring a fresh perspective to the game. New players also helps the hobby in general. Be patient with new players, though. We lighten up on a lot of our group rules when teaching rookies. More strict with veterans who play in our group.
14) Group harmony is strongly encouraged. Having a PC who doesn't get along with another due to legitimate role-play reasons is acceptable. A peaceful druid and a war-mongering fighter are going to have arguments once in a while. But excessive interparty conflict, stealing from other PCs etc. is a bootworthy offense if it doesn't stop. It causes bad feelings outside the game and disrupts play.
15) Communication is key. Players should tell the DM what directions and story arcs they would like to see their characters go in and likewise DMs should communicate some of their expectations to the players regarding the kind of game they want to run.
Thats all I can think of right now.
