The Simpsons Arcade is an unlock code game, so the unlock code expires and turns it into the demo. You could try re-downloading the game from the store for quick access to it since you say you still have PS+. Have you tried starting up a game that didn't use an unlock code? It should ask to check the license with the PS Store and renew it since you're still PS+, which would've then prompted you to buy it if you weren't PS+ anymore.
The games are labeled by the expiration date they had when you first downloaded them, so they should only require a quick check to re-enable them for your account.