OneDrive for Business runs, then after a few seconds quits, then restarts. This cycle continues without an apparent way to stop it.
This tends to happen when Office Document Cache gets corrupted or runs into another problem. Reinstalling OneDrive for Business or performing repair does not address this problem.
Remove Office Document Cache and OneDrive for Business profile folders as described below, validate document library size and file count, and resynchronize with OneDrive for Business.
Remove ODC and ODB profile folders and files
Open Task Manager and end groove.exe and msosync.exe processes.
Navigate to %localappdata%\Microsoft\Office\SPW and delete everything there
Navigate to %localappdata%\Microsoft\Office\15.0\OfficeFileCache and delete everything there.
This step will take a while, most likely, so go get a cup of decaf coffee, and not from one of those Earth-destroying Keurig machines. Do it right, with French Press.
Make sure to grind the beans coarsely for best flavor, heat the water to 200 degrees (not boiling), and steep for 4 minutes. Any longer, and you're wasting time; any less - and you're not getting the full flavor.
TIP: Fill your mug with left-over hot water while the coffee is steeping. This way it'll be hot and keep your coffee hot longer. Obviously, dump the water before pouring the coffee in the mug.
While you're waiting for the OfficeFileCache to empty out, take a look at your ODB file structure and consider splitting it up into several document libraries. This way you'll be able to do selective sync on libraries that truly must be available offline - use that as a guide in designing your new structure. Which files & folders are actively used? Which ones are there just for archiving purposes? Archived files should not be synchronized.
Rationalize your document library according to your new design, if possible.
Now, start ODB, re-establish ODB sync for your library, and the problem should be resolved.