As someone said before running 20 minutes is no where near enough time to recharge a dead battery. Most auto parts places will recharge your battery and load test it for free. Do that and then drive the Jeep over there and have them test the alternator on the Jeep for free. You might have a parasitic drain that is slowly killing your battery, you could have a bad rectifier in your alternator and it's not fully charging, you may have a bad battery. Have you taken off all your battery cable ends and cleaned them? I'm talking both terminals, the ground on the engine (may be two), the ground to the fender, the wire to the alternator, the wire to the PDC, the wire to the starter, all of them.