Ignore if not interested...
(Prot - it looks like you don't have the original radio, but this might help someone else if they do a search.)
Have you connected an Ampmeter to the battery system to see if something have a small drain
I would also consider a looking for a hidden current draw that is depleting your battery if you are taking the above into account and still having problems.
If I were you I would keep on trouble shooting until I found an answer to why your batteries are not lasting.
Those comments made me think of this service bulletin:
Service Bulletin NUMBER: 08-001-11 REV. A
DATE: March 05, 2011
SUBJECT: RER, REW, REP Radio Software Enhancements
This bulletin involves upgrading the software on the RER, REW, or REP Radio.
2010 - 2011 (DJ) 2500 Pickup
2010 - 2011 (D2) 3500 Pickup
**2009** - 2011 (DS) 1500 Pickup
**2009** - 2011 (MK) Compass / Patriot
**2009** - 2011 (PM) Caliber
**2008** - 2011 (WK) Grand Cherokee
**2008** - 2011 (KK) Liberty
**2007** -2011 (JK) Wrangler
**2007** - 2011 (JS) Avenger / Sebring
**2007** - 2011 (KA) Nitro
**2008** - 2010 (LC) Challenger
**2008** - 2010 (LE) 300
**2008** - 2010 (XH) Commander
**2008** - 2010 (WH) Grand Cherokee
**2008** - 2010 (RT) Caravan / Town & Country
**2008** - 2010 (LX) 300 / Charger
**2008** - 2010 (ND) Dakota
**2008** - 2009 (XK) Commander
**2008 - 2009 (HB) Durango**
**2008 - 2009 (HG) Aspen**
NOTE: This bulletin applies to vehicles built with an AM/FM/CD/DVD/HDD/MP3 W/ NAV Radio (sales code RER) or an MW/FM CD MP3 NAV Radio - EURO (sales code REW) or an AM/FM CD MP3 NAV Radio - ROW (sales code REP).
· The radio may lock up when a U-Connect call ends, this may cause battery drain.
· Intermittent no sound from audio system.
· Repeated **“Updating Channels”** message when in satellite radio mode.
· **iPhone4 (4.2.1) losing Bluetooth connection intermittently and not displaying accurate caller ID information when using UConnect**