I thought I washed my saddle pads often and I sure don't do them every week! I have several and I usually save them til I have a couple to wash together. When I was a kid and leased then owned a horse, the barn owner expected me to wash my saddle pad each time I used it. And it was a western one, heavier to wash than the English ones I have now.
Anyway, I can't see this lasting too long, if kids forget to bring them back,lose them or if other parents complain. Otherwise, though, I would probably just wash it by hand as others have said.