Have a look at some merchant facing (sales) documentation about account updaters [1]. I'm not affiliated (or even in the payments business, thank goodness), but this seems like a pretty decent overview of programs.
Maybe your issuer doesn't participate, but most do. Many merchants that do recurring or card on file billing will use these services because people often inadverdantly forget to update accounts and don't respond to notifications but do contact customer service when the renewal fails or their new order fails.