You have some good information below. To sum up, essentially it comes to this:
an as-is offer does not mean they can't back out on an inspection contingency
buyers can back out during the inspection contingency for pretty much any reason they want
the buyers' deposit can only be returned to them if seller(s) and buyer(s) both sign cancellation papers, but if they were inside their inspection contingency period and hadn't signed off you are likely wasting your time trying to keep it.