No one stole these cars when they were new and they aren't being stolen now. That said, just bypass it. I've had to do multiple passkey bypasses over the years, the early PK1 seems to fail eventually no matter what. At least they were very easy to bypass with some simple rewiring and disabling the VATS enable option in the ECM/PCM. Had to do it on both of my Camaros and just recently had to put in a bypass module in my brother's 99 Suburban due to the PK2 not working properly anymore. Its not worth the trouble of trying to chase the issue and finally fix it if you can even find it.
Our 99 Suburban did the same thing last summer - the module started to get throw a 1255 communication code after a dead battery and was never the same. It resulted in a pretty random no start situation once every few weeks, and usually when you absolutely needed to get in and drive of course. I just hooked it up to HP tuners and turned Vats off and it was all good. If somebody really wants one of these old cars the key cylinder security features are not going to stop them.