I have had this problem with a '96 Cad limo. Actually I was having several problems that at times would mask over the underlying issue. In the beginning the Antitheft Module was beginning to fail. It would shut the car down some days and other days it worked properly. Then the battery failed one morning just a couple hours before the car was to be used on a funeral, I sent it to a garage for a new battery to be installed. Then the pass key fault light would come on and off as the car was being driven. I sent it to an auto electric shop to have the system in their words "jumpered". They measured the resistance in the key and installed a resistor to "jump" the system.
Occasionally the car would just take a notion to not start, usually when I needed it the most! I then sent it to another garage and they verified that the electric shop had correctly measured the resistance and installed the proper resistor so the Pass Fault System was disabled. They then began a long investigation of the entire electrical system. They determined that the battery installer had installed a 700CCA battery which is 150CCA less than specs call for. (its 770 on a standard Cadillac and 850 on a Commercial Chassis).They replaced the battery with a 850CCA then installed a ByPass devise like the one mentioned above.
Lessons learned here: 1-Proper battery is a must. 2-See that the proper resistance is used in the "jumper" 3-investigate the Anti Theft Module 4-use competent repair shops.