One problem related to battery dead has been reported for the 2013 Jeep Wrangler. The most recently reported issues are listed below.
At the time I first tried out the vehicle & prior to purchase the battery was dead & it had to be "jump" started. I requested that a new battery be installed prior to delivery. I took delivery & about a week later went on vacation, did not take Jeep. It was not driven for about 3 weeks. When I tried to start it the Jeep would not start, as if the battery was dead. I jumped it & continued to drive it, every day for several weeks. After a few weeks, I let the vehicle sit for a day without starting and when I tried it would not start. 8/19/13 took Jeep to the dealer to get problem with electrical system fixed. They tightened the negative battery terminal & reprogrammed one of the computers. 9/2/13 Jeep would not start, had to jump it. Did not run it or try to start it yesterday. 9/30/13 Jeep would not start & when I jumped it the uconnect system would not work. . Took it to dealer. They think the radio is drawing current from battery. They replaced radio. 10/21/13. Jeep would not start after setting two days. Took it back to jasper Jeep. They are going to try putting a new battery in it under the assumption that the problem may be a battery post. Service manager checked the records and could not find where a new battery had been installed prior to purchase. 12/30/13 9:15am tried to start Jeep, it would not start. Got clicking sound like low battery, interior dash lights were on. There was a new dash warning light on, it is a red lighting bolt. 9:38am. Started it & after it was connected to "start car" for a minute it started. Let it run for a couple minutes shut it off & it started ok. Red lighting bolt not on. Found service bulletin issued by Chrysler, sept 2013. Bulletin number: sb-08-067-NHTSA item number - 10053694 10:30 am called about the service bulletin. The serv. Mgr. Will review & call me back.