That's a brilliant method, Michaels4gardens, I'll set that up for the next hutch. Right now there's two doors that swing together for each bunny space and that type of closure wouldn't work with two doors coming together. At the moment, they're held in place with a big nail.
You can see the nail in the one side of the frame in the back, but all the frames ended up getting the nails to hold them shut. I just drilled a hole through the bottom of the individual door frame into the face frame and dropped a nail in the hole. It works well, but sometimes the nail doesn't completely drop. I could drill the hole a bit bigger or use a skinnier nail, I suppose.
Your method seems like it would be easier to use.