Why did the letters keep coming?

I don’t think they did to be honest.

As far as I remember, Sy died and then Larry had a chat with Professor Finkle who, when asked, said he was still getting the letters.

There may have only been a few days between each of those events happening, so to Finkle, he still saw Sy’s last letter as relatively recent, i.e. still coming.

I certainly wouldn’t say the letters kept coming “long after” Sy died.