did you ever get a solution to this? i have a similar situation with my LC-65LE643U. if i use the RCA audio outputs to drive my external amplifier, the sound works as intended for a while, but then will suddenly cut-out. the audio is is dead at both the RCA outputs, and the TV speakers are also dead. i had connected the cable box audio output to the amplifier, and the TV never failed (with no RCA audio output connections). unfortunately, this doesn't work for any other video input (internet, usb, dvd, etc).
under sharp warranty, i have had the main logic board replaced, however the problem still remains.
power down/up resolves the problem, as well as a full 'reset'. any of this sound familiar?