A similar thing happened to me. The way I figured out how to get the "Media processing" to start up again is to make a change to the online family tree, so the Family Tree Maker recognizes the need to sync up again, and that way the Media processing will start up again.
I have a large tree with, I guess, a lot of media and the "Media processing" has been going on for over 24 hours, but I can see the progress bar continuing. I realized also, that I can't change to another family tree in Family Tree Maker or the Media processing progress bar starts over again. I don't know if that means it has to restart downloading from the beginning or from where it left off last.