I just found this on Hacker News: Burn-out visible in the brains of patients. Since I've suffered from burnout for about a decade, this comes as no surprise to me.
Try to do pushups until you can't do any more. Now, wait a minute, and then do 50 more pushups. That's the best way I can explain what burnout feels like--my brain just feels like jello a lot of times.
I'm sure a lot of other programmers have to deal with this just like I do.