My 2011 does this too and a new battery made no difference. It happens randomly, not just overnight -- sometimes I can just turn the car off and right back on without even opening the door and it will forget where it was.
It happens once out of every 10 or 20 starts and includes any random combination of:
- The main screen goes back to the main menu instead of wherever I left it (usually "CD" USB or BT audio)
- The radio comes on instead of USB or BT audio
- The split screen goes to GPS coordinates