I had a similar problem with my 2005 SRT-6. The BAS/ESP light would come on after about 5 to 10 minutes of driving and go off when the car was turned off. I took the car to the dealer and they replaced a leaking master brake cylinder and they thought that would take care of the problem. It did not solve the problem. I bought a OBD reader and found I had an error code (C1142 ABS Lateral Acceleration Sensor Open/Shorted). I replaced the sensor, cleared the error and took it for a drive and and the BAS/ESP light came on just as before. This would happen every time I drove the car. A few months later after the repair, the car would not turn over so I replaced the 3 year old battery. After replacing the battery, I have not had the BAS/ESP light come on since (over two years). I did test the battery periodically and it always tested good.