Could you try to remove the sync.lrdata file and restart LrD. This would restart/refresh the sync (metadata only).
Removing the Sync.lrdata might fix whatever the issue is. Or, at least, might trigger it to occur again. So remove the Sync.lrdata, start Lr, and then wait until it either syncs or gets stuck again and create at this point a Lr Desktop diagnostic log which can hopefully provide some clues.
You can find the sync.lrdata file here:
On Mac it's at /Users/<user>/Library/Caches/Adobe/Lightroom/Sync Data/Sync.lrdata
If you still have these problems please send me a LR Desktop diagnostig log - best as a private message with a downloadable dropbox link.
You can trigger the log via LR Desktop preferences -> Lightroom Mobile and when you hold down the alt key you will notice a generate diagnostic log button
-
Guido