@ xzap042
I am facing difficulty understanding your problem may be because you are not putting things in clear way. Anyway, after analyzing the data which you have provided let me put things in this way
Reasonable Arguments looks like this
1) Voltage across terminals once UPS is charging the batteries was found out to be 13 Volts for each battery
2) Your UPS stopped charging the batteries once voltage across the terminal reached 26.1 Volts. 13.05 +13.05=26.1Volts
3) 5- 10 minutes after once UPS has stopped charging the batteries the Voltage across the terminals were dropped to 11.8 Volts for each battery
First try to be clear once your are explaining your problem, secondly it can happen that indicators are wrongly connected that why once you think it is actually charging the batteries where as it is not and once you think it is not charging the batteries then actually it is charging the batteries.
1) Anyway if my assumptions are right as stated above, then you need to understand that UPS should stop charging the batteries once Voltage touches 28 Volts for both the batteries where as in your scenario it looks like it stops charging the batteries once Voltage touches 26.1 Volts.
2) Once UPS has stopped charging the batteries and that in your scenario is at 26.1 Volts then obviously Voltage will drop to 11.8 Volts or 12 Volts after 5-10 minutes.
3) Normally once UPS will stop charging the batteries at 28 Volts then after 5-10 minutes once you will take the measurements of Voltage across terminals you will find that it has dropped to 25 or 24 Volts which is absolutely normal.
Rest you need to check the current charging rate for that you need to quote
1) AMP –HR rating of the batteries
2) You will need an AMP meter
Go back to the thread and looks for the image of AMP meter already posted in the thread.