I never was really burned out because life made that I was out of permanent internet connection for 3 years. During that time I was playing games against the AI (if you pickup your scenarios carefully and buff it up a little like +1 / +25% it can be a real challenge - other good thing is that it never disappears in the middle of a game because it's loosing...) and also had a friend with whom we played IP games with direct link between our rigs.
I had completely stopped for the last year because I was playing other things (mainly the Total War series) I am back to business because I can now have a regular internet, but in order to avoid the burn out syndrome, I don't take more than 4 or 5 games at a time. If you play seriously, this is already some work, but as your opponents also have a real life, you get to play around 3 turns a day. Since my present job allows me to play 18 hours a day (keep 6 for sleeping) that's not too much of a burden and I can still play other things besides. And spend a lot of time writing blah blah on the forum...lol