Popping in from August to say I'm washed the cover to DD's Roundabout a few times now. Delicate cycle, and I hang it to dry. Hasn't seemed to cause any problems, though getting all the straps back in place is a bit tricky the first time. You might borrow a tip from my car-repairing hubby - take pictures of it before you start disassembling it, and maybe a couple halfway through. Because sure enough eight hours later when the cover's dry, you're not going to remember just where that certain strap belongs.
Be sure to take the instruction manual out of the little storage pocket BEFORE it goes through the wash. I learned that one the hard way.
Oh, and safety technicians say you should never, ever wash the straps themselves. Something about it weakens the fibers. I'm not sure I'm sold on that, but I thought I should tell you that's what the experts say.