Hi, thank you for choosing Justanswer, I look forward to helping you resolve your issue. First I need some information from you.
Do you ever have a problem starting your Jeep such as a dead battery? Do you ever have to jump start the Jeep? Are there any other indications other then the battery warning light and the lights flickering and/or the radio shutting off that there is a problem?
Ok, I take it then by what you have stated there is no real issue with the battery loosing its charge etc. and for starting it starts like any other vehicle starts. Not slow cranking like a battery that is going dead etc..
The first test I would like you to do when the problem is occurring is to measure the voltage across the battery posts with the vehicle running.
Ok, it should be over 13 volts with the Jeep running especially if you had the lights on etc.. So do test it again the next time it is acting up so we are sure of what it is. i am thinking the PCM is not telling the alternator to charge the battery but do not want to send you down the wrong road so really need to know for sure exactly what the voltage is across the battery posts with the Jeep running.
Sounds good, I will keep an eye open for your reply and get back to you as soon as I can.