You are right Staigen, if it is a horizontal line you'll have to check the vertical amp and its surrounding if the line is vertical it might be a cold solder joint in the horizontal part, usually not so troublesome.
What brand is it and model?
We had exactly the sam problem with our Panasonic TV an it was still within its warranty so we took it back to the shop and they fixed it. There was a bad solder joint on the vertical amp, I put this down to poor build quality.
