Theft light staying on car starts right up

Theft light staying on either car locked or unlocked, car will start right up, check all fuses under dash and hood, tried two ways to reset theft system, replaced ignition switch and transceiver ring, what could be next to check!? 2003 Mach One
 
Would that be an actual key failure? I heard the chip keys don't last forever - it has been mentioned to always keep a GOOD second key in a faraday bag or pouch somewhere, so it can't be read from a distance, as the original key will eventually fail - mine started to do so at about 200,000 miles, had a mobile locksmith come to my condo complex to program a couple of new keys. I understand it is cheaper and easier to program a new chip key IF you still have a good working existing CHIP key.