If it the original battery in the car from the factory they were bad for internal bad connections on the battery ...
You don`t have any anti theft lights on do ya >?
There was also a problem with the key cylinders having a loose wire for the theft system sometimes having a code stored ...
Will almost have to duplicate problem and check to see if voltage is @ starter on purple wire when it happens ect.
bg 25 years MAster tech GM, January 2006