The 12V TV outlet may not have big enough wire for the inverter, so the voltage drop across the wire is to much.
Not sure, but I think I herd somewhere, that on 12V power you could not use humidifier.
I have wonder about smaller inverters to just run the CPAP machine. My 2500 Watt inverter draws about 120 Watts just being on. Since we have Six 6 volt batteries and solar, we haven't been to worried about it, but last year we dry camped, and never saw the sun for three days (only 15-20 Watts out of solar panels), and had to crank up the generator for 5-6 hours to charge the batteries.
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