Battery/charging issue
So I go driving in the woods with a couple of other jeepers yesterday. I drive 20 miles or so to my buddies house. When we leave, jeep starts. We drive 15 more miles to the starting point and stop. Jeep does not start. It acts like the battery is dead, with the starter barely turning over. I get a jump start and everything is good. 7 more miles we stop. I wisely park facing down hill. Go off to do some sight seeing. Return, and the jeep won't start. Roll start it down hill and it runs. As I am driving along and it is Oregon, I have the wipers going and the defroster going. These slow down so I turn them off. At our next stop I have one of my buddies hook the jumper cables up and leave them hooked up for a few minutes. Jeep starts and off we go. Drive another 45 minutes then stop. This time the jeep starts on it's own. We drive and stop after an hour or so and eat lunch. After word the jeep starts on it's own and the wipers seem to moving the correct speed. At first I thought my battery or alternator was bad. I have never heard of a battery, stop being bad. Does an alternator stop working then start though? Any ideas are welcome.