One more thing you should try - when you connect the module to the car, make sure that:
1. LED1 starts doing disco
2. Once you see that, open your phone's Bluetooth settings and pair to BlueSaab.
I believe the issue you are seeing is because RN52 is programmed to go to sleep if it doesn't see any device for X seconds.
2001 9-5 SE V6; 2006 9-5 Wagon; iOS; BlueSaab version = "latest and greatest" :)