Yes, to the ATF.
If its not reported, its going to stay on the books, and that could cause some bad feelings if you're ever asked to produce the registered item.
especially the further down the road you get. "that one? oh, it broke 8 years ago, so I just threw it out..." isn't going to go over real well with the Feds.
I can't point you to the specific law, section and line but I'm sure there's some kind of reporting requirement for "lost, damaged, destroyed, expended...(and stolen, too..)
The ATF deals in that kind of thing all the time, they understand stuff wears out and breaks. They also understand well, that things get used up. They also regulate bombs, grenades, rockets, artillery shells, tank gun ammo, and all similar things.
Here's an interesting tidbit, cannon, bazookas, tank main guns mortars, and such are NOT NFA items. However, each round of exploding ammo IS!!
And they have a process in place to account for people actually firing
the rounds, and updating the registry. I knew a guy, decades ago who had a couple cases of legally registered hand grenades. Every year he would use 2 or 3 doing demonstrations. If I remember right (and its been ages), he said he just told the ATF where and when he used them up, and everything was cool. HOWEVER, he did have to tell them, and not wait a long time.