2 Step Verification or 2 Factor Authentication?
2 Step Verification - from the article below.
If you ever need a new Recovery Key, you can create one from your Apple ID account page. Just sign in with your password and trusted device, go to the Security section and click Edit, then click Replace Lost Key.
Apple ID - Two Step Verifications FAQ
2 Factor Authentication doesn't mention generating a new Recovery Key. Have you tried turning Recovery Key off, logging out/in, and then turning it back on?
How to generate a recovery key - Apple Support
Two-factor authentication for Apple ID - Apple Support