Yes. Weekly and monthly league prizes can be claimed for 90 days. After that, an unclaimed prize goes back into the league prize pool.
Weekly airdrop wins can be claimed for 60 days. After that, unclaimed drops go back into the airdrop pot for a later week. Major War League prizes do not expire.
A reward that can no longer be claimed is marked Expired in Rewards and claims, so claim your rewards in time.