Not a possibility for most of us - but many professional longarmers have two (or more!) longarms. Usually one is for free motion quilting, and the other uses robotics, so both can be busy at the same time. I'm sure this also helps if one of the machines has to go in for service.
joe'smom - as profannie said, the longarm consists of a machine head, a frame, and a carriage that the machine rides on. For servicing, the machine head (and sometimes the carriage) can be removed and taken to the shop.