Tivo Roamio OTA stops recording when TV turns off

I believe I've answered my own questions thinking about this while lying in bed last night:



-Sometimes when I record a program when I'm not home, The program doesn't record and the "History" menu says "no signal". But when I turn the TV on, the signal is fine.



and



-While I'm watching a program and I go to bed early, I press "record", turn off my TV, and go to bed, only to see that the rest of my program DID NOT record.



I believe this is happening because when I turn off my TV, it also turns off my amplified Mohu Leaf 50 antenna. My antenna is plugged into my USB port of the TV so when the TV goes off, so does my antenna, therefore no signal to my Tivo and no recording.



Does this sound logical or could there be some other problem? Thanks!!