I have seen this problem before, but I still don't see an answer that is usable.
I have a Latitude 7350. I bought the Dell Active Stylus 750-AAGN. From the start, it would work for a while, then stop. I'd take the battery out an then replace it and it would work again. Now even that fix isn't doing any good.
The stylus is only 3 months old, and is used only occasionally, so I can't believe the battery has run down.