Handoff of completed Reminder items not working?
To clarify - Syncing reminders between apple devices is not part of handoff. It is based on iCloud sync only. Handoff is something that happens when your devices are on same WIFI and also use same apple id as primary iCloud account (Concept of primary iCloud account applies to macOS only as it supports multiple iCloud accounts). Calls and messages use Handoff.

Solution 1

Now to your problem, you might have multiple apple ids (accounts) on your devices and reminders might be using different apple ids in different devices. 

To verify on your macOS - 


Goto System Preferences -> Internet Accounts
Check the iCloud accounts and make sure the correct iCloud account has reminders enabled.
If you are using more than one iCloud accounts, then open Reminders app on macOS and check on lists on the left menu for the
iCloud account being used. It would of the format iCloud (&lt;account name&gt;). You could also migrate the reminders to correct iCloud
account by drag/drop and then uncheck the unwanted iCloud account
for reminders in settings as stated in (1) &amp; (2) above.


To verify on your iPhone - 


Goto settings -> iCloud
Make sure reminders is turned on and the account is correct and same as on macOS


Solution 2

Toggle reminders in iCloud settings on your devices one by one and see if the sync starts again. The steps to access the settings is same as above.

Hope this helps.

Update: Added second solution of toggling reminders