I can answer your question in multiple ways, first who told you to reduce the cutoff to 13 Volts, did you check the voltage on battery terminals, I guess no. did you verify the charging rate, I guess no. lets assume, that charging rates and cutoff is set properly and as per batteries specification( I have my doubts) . Even then UPS does not cuts of charging as Voltage never reaches 14 Volts then this means your battery is dead and you need to replace it because as per your question its seems like that you have figured out what the issue is and above can be a possible answer. Using a dead battery with UPS systems doubles your electricity bills and in return you don’t even get any backup time.
Without knowing the charging rate, amp-hr ratings of your battery, cutoff Voltage set on your system and voltage on battery terminals while being charged, time its taking and UPS still charging the batteries. You cannot tell what the problem is with your system.
You want to shoot in air then go ahead.
