Depends why you have the burn-out. Is it because you are creating sites back-to-back and now all your ideas are starting to look the same or because you are working in-house and are on a one-brand-track mind and the creativity is slipping away?
If you are simply designing so much that everything looks the same -- take a break!! You have to work this into your cost analysis of running a business. You need to take two days and do NOTHING web design related. Do artistic things, just get away from that computer and stop thinking about it (i know how hard that can be to turn it off). Two days might sound like a lot, but I am assuming you are much like myself, perhaps designing or developing a couple of sites at a time always with another to be started when one is completed.
If you have in-house burn-out -- you don't have to leave your job, but you SHOULD start freelancing. Get some variety into your system and let your creative mind explore a little outside the restrictions of the brand police. You need it, you crave it and it will keep you sane!
I've got a great boss who's also the project manager, and he does a good job of keeping me balanced between developing and designing. I think a lot depends on where you work and for whom you work. I definitely feel lucky to have the guy above me say, "Don't worry, Colin, I'm working on getting you a big design project." This makes him a great leader, I believe. So, I haven't really hit too large a burnout. I was before this job. Boy, was I!
During the time you work I think it's important where you work. I get tired of my office space from time to time and I hate staring at the same view. That's when I get my work synced with my notebook and get out to a different space: a wifi enabled coffee house (work wonders with me), a place in a park, someone else's office :). It all depends on what you like.
I found that changing the work place, even for a brief couple of hours, keeps my mind fresh and agile.
I have the luxury of being a freelancer so time management is up to me. If you are employed somewhere this might not work for you.
I second with what others said: take some time for yourself away from the computer. Do things that are fun, relaxing and refreshing.