Do these points expire?  If not, should they?

They don't expire, but they can be taken away by other players who may later become higher ranked than you.

And to answer the second question, no. They're based on rankings, which should stick around as long as they're relevant. In the long run, there will be some downward pressure on rankings for players that don't play any more as more people play and win games, making it harder to get to the top of a given board ladder.