Do purchases expire?
No — purchases don't expire. A book you've unlocked stays unlocked, and you can re-export it whenever you like, indefinitely.
Worth separating from a question that sounds the same: files we host for you do have a window. A cloud backup keeps for 60 days from your last edit; a Concierge kit stays downloadable for 30 days after your first download, and the Concierge copy in My Books for 90 days from delivery or your last edit. That's how long we hold a copy — it has nothing to do with what you own. When a hosted copy comes down, the license is still on your account, and re-opening the project file re-unlocks every tool on that book. See Do you store my manuscript or cover files?
The only way to "lose" access is to lose the license key — for example, if you were never signed in and then cleared your browser data. To prevent that, sign in: your keys are stored with your account and sync to any browser you sign in on. You can also always find them under My Books → Purchases & license keys. See Where can I find my license key?