We are having generator problems on a few models fact is some now have recall on them not sure if liberty is on the list or not. Yes it could be the battery but the alt needs checked the charge but duty cycle, you need to have put on scanner have the generator duty checked more than likely it will be at 100% if thats the case thegenerator needs replaced. If it is charging at 100% it is charing only volts not amps.
Check with dealer may be either covered under powertrain warrenty or posiably recall(i dont what models or years are covered) Make sure the battery is checked real good not bu just volt meter or a load tester as a bad battery will eat generators fast. We use a GR8 tester it will test the battery generator starter in a single operation.
Melvin Schwentner
Chrysler mastetech
A.S.E certified mastertech 30 years
2013 chrysler 200
2005 jeep liberty limited
1965 chrysler 300 sport
1951 desoto s15 custom
2015 viking FQ