The only time i had a tv fail on me is when a lightning struck the antenna, back in the country house.
It was an semi-modern CRT, and got fixed pretty quickly.
Never seen a flatscreen TV failing, however by the time they became affordable i wasn't watching tv for more than an hour a month.
A flatscreen monitor, however, fail twice.
First time it was a second generation (first generation that didn't cost multiple kilodollars) one, and it failed with occasional white screen on turn-on.
Other time it was a surplus store register monitor - a tiny thing i bought on a flea market for various debugging - which supposedly spend a decade doing nothing in some warehouse. It also failed by gradually refusing to turn on, with white screen.
Not to mention two times laptop screens failed.
One time on nanonote thing, where it started loosing clocks:
That got fixed when i dropped the thing onto a hard floor.
Other time on a Sony Vaio pocket "laptop", which had some sort of prototype AMOLED display - this one would suddenly start showing garbage. Got fixed by placing a piece of rubber on the back of the connector.
...So, yeah.
Flat screens do in fact fail every now and then.
But they can also work well - the first flatscreen monitor i had, of the first generation (the one that did cost multiple kilodollars per 17" screen), is still working after 15 years or so of service in several places.