go look @ This THREAD
I believe there are 2 parts to the keyless entry system:
1. Keyless - unlock the doors, period.
2. Anti-theft - adds shock sensor and starter interrupt.
I'd disconnect the shock and starter interrupt @ the module - as shown in the pics - and see if that solves your issue.
Or you may need to buy another module - yours may be 'dying>>>dead'. I have one if you want to test it.