I'm playing 1.16.4 on singleplayer survival mode. I do have a few other mods installed, but this happened even before I installed other mods.

When I enter my world, the mod works great, chop chop, trees felled rapidly, great fun had by all.
Randomly though, the mod just stops working. I tried to find a reason, like maybe moving axes in and out of the inventory messed it up, or getting attacked stopped it working, but eventually found nothing really connecting these occurrences.
Deactivating and reactivating the mod on the same axe or a different axe doesn't help. The only solution is, to exit my world and then get back in. Then it works again, for a random amount of time, then I have to repeat my exit/enter solution to get it to work again.

While this MAAY be a workaround, it really should be fixed. Awesome mod though! Grateful to the mod dev for making it.

Crouching will toggle the Timber mod when it is activated. Try cutting the base of a tree while crouched, replaced the block, uncrouch, crouch again, and the mod may begin working again.