Hopefully he has time to calm down
He may be worried about the costs of repair.
If you are happy, and can convince him, get it repaired and bear the cost yourselves, no matter who it ultimately belongs to.
I think this is the most expedient thing.
It does sound like your neighbour is suffering a little, and possibly could do with some help from a kindly referral to social services. ( aged care)
We have fence posts with the cross bars and planks attached. One of these was giving way, and I asked my husband if we could just install another post, next to the one which was less stable.
That wasn’t an option, and he was quite rude and nasty about the idea, until talking about it with my brother, who confirmed it was a good option, and this is what my husband did.
It was a cheap repair for us, and doesn’t look odd, that there are two posts together.
Men !! ( mine hasn’t even got old age as an excuse )