Double stick tape and what ever you choose to stick it to works good. Wood , a stiff rubber block or what ever you can find that fits in the area that you need to sand. Get the good indoor stuff for carpets , it works better. The all weather stuff is thicker and hard to cut with a very good glue on it.
You should be able to peel off the tape from one end and then reapply a new piece of sandpaper and tape.