Anti thief light is on

If the light is staying on but the car isn't shutting off there is a parts failure in the system. However it could shut down the car at any time depending on the failure. The first place to start would be with a dealer level scan tool, it can look at the various parts in the security system and show where the issue is. This usually means that the issue isn't a bad key or ignition related failure but in the intrusion alarm part of the system.