I read about the living items and how if their morale is low you have to suppress them to get it back up.

For the jackboots, it seems it drops by 5 for every battle, and no way to bring it up outside of suppression.

My question is though: I have the Jackboots morale now at 0, but it's still equipped. Does it mean it's still working? How do I know when an item stops working due to bad morale?

A bit late with the answer but...

Out of control items don't give any bonuses. Easily checkable with items that do something visible.

The thing is: they still do show up in your creatures' page.
If you have out of control Jackboots and look at Robbers in your inventory, you're going to see that they do have bonuses. It's only when you enter battle that you see the bonuses aren't there:

https://www.gog.com/forum/general/kings_bounty_items_with_low_morale