There is a way to backup and restore linked trees in FTM, but it may already be too late if you didn't create the correct backup copies.
Here's how you do it:
(1) Copy the contents of your /Documents/Family Tree Maker/ folder to a backup location (or a specific .ftm file and its associated media)
(2) Copy the contents of your /User/AppData/Roaming/FamilyTreeMaker/ folder to a backup location
When your sync goes poof, you copy all of these files from your backup location to where they were originally. This will overwrite the broken stuff. Next time you run FTM, it will be in the same state it was when you copied all of those files to your backup location.
Unfortunately, if you backup you tree in the way that it is *designed* to be backed up, i.e., by creating an .ftmb file, then you will break the link, and you will have to redownload/upload. Stupid, eh?