The 10.5VDC will have an effect on the inverter output. Most inverters are designed to produce 115VAC with a battery voltage of 13.2 VDC. Unfortunately, when the battery voltage drops to 12VDC (under load) the output of the inverter may be somewhere in the range of 100VAC, when the battery is at 10.5VDC (this is a DEAD battery, SG = 0), and the inverter will shut down.
The Fridge compressor (compressors in general) is designed to run at 110 to 120VAC. When the voltage drops, the compressor has to work harder. Add the known issue that the fridge compressor runs longer and hotter on a regular inverter (non pure sine wave type), the battery will discharge a lot faster.
As mentioned, I would check the output of your TV's trailer plug to see if it is producing the needed voltage/current. Adding another battery of the same mfr/Ah rating may get you a few more hours.
Don
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