The snap refresh command is meant to refresh any available snap but it doesn’t fail if one of the snaps can’t be refreshed. If you tried to refresh that snap specifically with snap refresh snap-store, then the error would be surfaced. Next time you see the notification, you can either kill the snap-store like you did to trigger the automatic refresh, or you can just run snap refresh --ignore-running snap-store which will tell snapd to ignore the running snap.