Jeep towed discharged when towing. This is new.

Jeep manuals are way out of date on some topics. My 2015 manual says to leave the key in ACC but there is no need to do that since about 2008. UNLESS you need power such as the Brake Buddy. However, not sure it would drain you battery unless you were doing lot of hard stopping or the sensitivity is set to high. I do think you should pull the battery and have it checked and check the charge line.