Definition: A regression check is an automated check that confirms existing behaviour still works after changes. In ATDD, an acceptance test becomes a regression check once its feature is accepted, and it keeps running from then on.
So what? Repurposing acceptance tests as regression checks gives them lasting value. If they're left out of the automated release process, they go stale and soon nobody wants to run them.
Examples: Adding each passed acceptance test to the suite run on every build. Fixing a failing regression check immediately rather than letting broken tests pile up.