Correct, the transaction only stays on your list of eligible travel expenses for 120 days. After that time, you still have your points, but you can't spend any of them towards that expired transaction.
@disneedee has a good point about keeping in mind how long it might take you to accrue the 10,000 points needed to redeem against a new charge. It depends on how quickly you think you'll rack up additional points.
In my case, if I have 50,000 points, I'll pay $432 towards my hotel bill, which earns me 864 points. Then I'll redeem 43,200 points to wipe away the $432 hotel charge and get a 5% redemption bonus of 2,160 points. This leaves me with a balance of 9,824 points. I'll make a second payment of $101 towards my hotel, which earns me 202 points. Once those points post, I'll have a total of 10,026 points, which I'll redeem towards the $101 transaction. I'll be left with 501 points in my account after I receive the 5% redemption bonus.