Per comments, it sounds like you observed a 1V drop in the wiring under moderate load. The number one problem I see with inverters (A UPS is basically an inverter) is that the DC wiring is too small. As current flows through this narrow wire, voltage drop occurs. This is especially obvious during heavy loads. The inverter (or UPS) doesn't know that the voltage drop is due to wiring. It thinks the battery voltage is low and gives a warning or shuts down.
The best way to avoid this is to use adequate sized wiring. The size depends on both the length of the wire run and the diameter of the wire.
Let's go through a quick example. If you have a total of 20 feet (including all wire, both directions plus whatever wire connects the two batteries) of 12AWG wire, how much resistance is that and what voltage drop will it cause?
First, find the resistance of 12AWG wire online in a table:
http://bnoack.com/index.html?http&&&bnoack.com/data/wire-resistance.html
That table shows 1.7 Ohms for 1000 feet of AWG 12 wire.
So for 20 feet that will be 1.7 * 20 / 1000 = 0.034 or 34 mOhms.
Now let's say the current is about 6 Amps (to approximate your 120 Watt load, and allowing for efficiency of the UPS). The voltage drop will be equal to the wire resistance * current:
6 Amps * 0.034 Ohms = 0.2V
That may or may not be enough to cause a problem at 6 Amps. But for a larger load, like 20 or 30 DC Amps, it would definitely be problematic. This is why even small inverters typically have large DC wires.
Moving the batteries close to the inverter also helps a lot.
A final note: The termination of the wire (crimp, solder lug, etc) can often become a point of high resistance, especially when currents are high (10, 20, 50, 100 Amps). It is a good idea to monitor the temperature of high current connection points to make sure everything is OK. They can actually get so hot they become a fire hazard.
