Tidy Plates will track and display your debuffs, so long as it can
associate the nameplate with the combat log data.
Losing the timer on a mob usually occurs when the nameplate has
disappeared at some point from moving off screen. Mousing-over a
nameplate restores that link. Tidy Plates can automatically restore
links on mobs that are marked with a raid icon, and enemy players
(since they have unique names).
If the debuff tracking is being lost, even when the nameplate is
visible for the whole duration, it would have to be from new combat
log data coming in and overwriting the expiration time.
If I knew what to change (if it's possible to fix), it'd already be in
the addon. Perhaps you have an old version? Grab the latest version
(from Curse.com, v6.3.5)