Licenses should definitely be tied to your PSN account, but specific downloads are likely tied to profiles. So if I'm understanding this correctly you made a profile, bought a game, deleted that profile for whatever reason, made a new one with the same account, and now you can't play the game? You probably need to re-download the game, since it's currently associated with a profile that no longer exists on your console. Even though your new profile is made with the same PSN account, the already existing download doesn't automatically get associated with it.