Does a QR code expire?
As long as the short link behind it is active, your QR code will keep working. There's no expiry baked into the QR itself, so codes you've printed on flyers, posters, or product packaging will continue to point at your destination.
What scanners see does depend on your plan's click quota. Once you've used up the clicks included with your plan, further scans land on a "closed" page instead of your destination until you upgrade or the next billing cycle starts. See What happens if I exhaust my click limit? for details.
If you want a QR code that deliberately stops working after a set number of scans, use Redirect by Click Count to cap the link at a scan limit. Once the limit is hit, further scans land on your fallback URL. See How to generate a QR code that expires after a certain number of scans? for a walkthrough.