Sometimes this works, sometimes it doesn't. Probably a life lesson in there somewhere. (Thanks, Wind, for finding this)
Open Synergy and go to Gradebook --> Gradebook Main and click on the colorful Google icon.
Then click the gear icon.
Scroll all the way to the bottom, and check the "All Classes" box.
Click "Done" and hopefully enjoy having that much less stress to deal with.
According to the info button in that screenshot, Google only syncs assignments due within the last 30 days. Including all classes and hitting the Resync button overrides that behavior, because nothing is late anymore. Wind says that option didn't used to be there, so I'm guessing Synergy is trying to catch up to Google's flightiness, bless them.
If THAT doesn't work...
If Cruel Fate thwarts your efforts, you can also try resetting your Classroom code, feeding the new code to Synergy, and rerun the sync. In some instances that has resolved issues as well. Christina at the DO found this stratagem in the Synergy help desk, where it reputedly worked in at least one case.