Sounds like either a component fault on the PCB (unlikely) or the most common fault that causes this - a worn or dirty contact on the headphone socket.
I have this problem with my protable in my bedroom, I occasionally use headphones, and the cheapo connectors manufacturers use wear down quickly - the main speakers are switched off when the headphone socket is inserted, and sound is fed only to your headphones.
When the sound goes off on my TV, I usually throw stuff at it, or hit it. If I must, i get up and wiggle the socket, or touch it with the headphone plug & all is well for a while.
The repair is simple (I'm just too lazy, but I am sick of seeing PCB's all day as I am an engineer) You could either spray your headphone plug with WD40 a few times & plug it in & out a bit - this will solve the muck problem.
Take it to bits;
(only if you know what you are doing!!!!! - seriously, you can be killed / injured / thrown across a room by voltages in a TV),
and clean the contacts with WD40 and a cotton bud or something.
(or go to an electronics shop & buy a replacement socket & fit that)
Best bet is to find a local electronics geek (like me!) and have them fix it for scraps of food... or money...
(Hope this helps, have never used this 'forum' before - was actually after boiler help, but thought i'd pitch in :)