OK so you bought the car used? was is from a dealer? or 3rd party?
and im ASSuming your car did NOT come with IR headphones when you bought the car yes?
can you post the brand/link to the headphones you purchased?
so ASSUming you did not have any ir phones when you bought it, you were only able to test the IR function once you received the phone you bought from amazon yes?
i ask about the flip down screen because there is a company, Myron&Davis, that makes aftermarket audio/video solutions for these (and other) cars.
thus, if this was installed AFTERmarket, either at the dealer by a 3rd party or the care owner, the wiring is going to be different than factory.
if you can, would mind taking a shot of your monitor setup? i don't mean to make this difficult.
one thing to try: get the dvd running throughout the sound system, making sure the balance controls are all turned to the center. once the sound from the dvd is playing in the cabin speaker, push the button on the dash to set to REAR and test.
could be the family of IR phones you purchase may not be working properly (rare).
silly but kinda useful question: when you put you had over the IR sensor on the headphones. does the sound get muffles/make static? does it do this on BOTH L and R channels in the headphone or just the left?
another RARE possibility could be the IR sensor in the screen is loose inside (wiring). constant flipping up and down of the monitor may have case some issues. maybe try a light tap tap tap around the monitor bezel while wearing headphones.