A quick update. This is definitely related to the Apple Watch. If my Watch (series 3 running WatchOS 6.2.1) is off at 09:00, the categories don't disappear.
If my Watch is on, they do. What's more, any status such as "Waiting for" against a Task is wiped out at 09:00 along with the categories.
I think this has something to do with the Today Notification feature added to Reminders at iOS 13. By default this runs at 09:00, and it's as though
this is still doing something to update the Tasks at 09:00, even if it is switched off in Settings. When this syncs to Exchange, the Tasks are updated, minus Categories which, of course, Reminders doesn't support. You can see the Tasks are being updated
at 09:00 (by looking at the Modified Date through Outlook).
Further, even with my Watch switched off, if Reminders on my iPhone are lagging behind a bit with changes made elsewhere (and let's face it, they normally
are), at 09:00 the version on my iPhone is "merged" with the version on my Exchange account. For example, if I remove a Category on the Exchange Task and replace it with another, but the change hasn't yet sync'ed to my iPhone, at 09:00 the Category re-appears
against the Task, alongside the replacement.
So, in summary, I think the sync'ing of Exchange Tasks to iPhone and Watch is pretty much screwed, and I have no idea how to log this with Apple. And since turning off my Watch just before 09:00 every day is not really an option, I guess I'm
back to switching off Reminders sync for my Exchange account until a fix arrives.