Maybe it hasn't had enough time to recharge off the converter? You could try turning off the converter and using jumper cables off your TV to see if there are no bad connections in the A-frame area. Electrolyte level okay? You can use a voltmeter to see what the state of charge is and what voltage the converter/charger is putting out. With 120 volts to the converter turned off (at converter panel), use a voltmeter to see what voltage is showing up at the converter from the battery (take front panel off converter) - do this with no-low DC load and then turn on a bunch of DC loads.
Last year we had our battery develop a bad cell in under a year. Would not hold a charge. A battery shop diagnosed it. You could take the battery to a battery shop for testing.