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