This happened to me. I left the dome light on overnight, and it was stone dead in the morning. I was able to jump it to get it started again, but as you noted, I had to keep the RPM up for about half of my drive to work (about 10 minutes) or else it would try to stall again. By the time I pulled into the parking lot at work, it seemed to be working normally. When I went to go home at the end of the day, it would not start at all, despite plenty of charge, and many repeated attempts. It was throwing a code, so I called the service dept. at the Jeep dealer and had them look it up (I carry a xerox of all the error codes now), and it turned out to be my old friend, the camshaft position sensor. I decided to make another attempt at starting it, and to my surprise it started, but once I got it home I did not try to drive it again until I changed out that sensor.