Battery Saver Mode
I found one You tube video that says disconnect the battery to let the computer reset.
You could reset the BMS, and maybe that'll help the truck re-learn the battery. This makes the most sense if the battery has been replaced recently.
You could charge the battery to 100% using an external charger and THEN listen to the radio for a while and see if you get more listening time. This is probably the lowest effort solution.
You could take the battery to get tested, because maybe it's not as "good" as you have assumed. Some people report weak batteries in brand new trucks, or defective brand new aftermarket batteries. There's no easy way to tell without testing.
Battery less than 1 year old and tests out fine and the condition did not start until apx 6-7 months after the battery was replaced
Can the BMS disable the rear window defroster? because this seemed to stop working about the same time now that I think of it, I originally thought it was a fuse or the switch but I checked all of the fuses and they are good and sometimes when I turn on the rear defroster it works for a few seconds(switch illuminates) and sometimes it doesn't
Ford Battery Management System or BMS
If you have a 5.0 or a 3.5 Ecoboost unplug the BMS and charge the battery up with a trickle charger overnight and then see what happens, the 6.2 does not have the BMS. I guess they didn't figure it was going to help on the gas mileage on it

I don't know if the 2011's did it but on my 2013 you can turn the radio on without the key being on also so it uses less juice.
As for the rear Defrost, sounds like a loose wire or connection, mine quit working completely right after I got the truck. I need to take it in before my Extended Warranty runs out and see if it and the sunroof are covered.








