Well the display shouldn't have anything to do with it. I do suppose there is an off chance the TV is throwing some EMF interference causing it. Does it do it when the display is comepletely turned off. Try that just for diagnosis purposes.
I'd try a different DVD player for sure if it still drops out with the display off. Even a cheapie you can return would probably reveal the drop out issue.
With the display off, if it does not drop out, an Ultra ultra shielded cable routed as far away from the display as possible would be the only thing to try. Beside possibly returning the display.
