No reason to take it out as long as it's not turned on creating condensation.
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2013 Z-1 251BH | 2011 Nissan Armada | Curt WD hitch with no sway control 2014: 20 Nights & 1338 Miles 2013: 23 Nights & 1200 Miles 2012: 10 Nights & 254 Miles
The only reason I can see for taking the TV out is if your trailer is stored in a place that is not totally secure and it could get broken into. It happened to someone I know. His TV was stolen. It was some kind of storage lot.
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2012 Cruiser Sahara 330SS
2015 F250 Super Duty diesel