Like Bitly links, QR Codes you create in Bitly never expire.
If you use a custom domain to shorten your links, they will continue to work as long as your DNS is still pointing at Bitly and the custom domain is attached to a Bitly account.
A QR Code will stop working if you delete it or the associated short link. If you redirect the short link associated with a QR Code, the QR Code will also point to the new destination URL, rather than the previous destination.