One problem related to battery dead has been reported for the 2011 Dodge Ram 1500. The most recently reported issues are listed below.
Just took my vehicle into the shop on 2/17/15 due to the battery being dead as a result of the fuel pump running all night. Aaa certified shop just informed me it would cost 1600. 00 to replace the tipm and program it for my key etc. There is a faulty fuel pump relay inside the tipm and I have to replace the enitire module. This issue is most likely related to the durango/Jeep recall for the exact same issue, as well described in the class action lawsuit. It is not covered by any warranty.