I have noticed some of the defogger lines in my rear screen have broken. Is there any way of repairing them. I believe there is a kit where they can be painted on. I have looked for a company that can repair these but cannot find any.

Those conductive paint and pens for fixing rear window elements are pretty terrible. If you can clearly see where the breaks are in the element, it would not hurt to try. But TBH, you are better off having the rear window replaced or simply making do and living with the broken element lines (assuming it’s not so many that are broken that it renders it useless). 
 

However, if it’s the whole rear window element that is not functioning, it may not be the element at all, but rather one of the two (or both) of the metal spade connectors that come off the left and right hand sides of the rear window making a bad connection with the sockets they plug into in the window frame. They can shake loose over time.

I used some conductive paint probably 40 years ago, I bet I still have it somewhere

 

It worked well but as would be expected was a higher resistance than the printed element, as such on initial demisting the repaired bits would clear first & then the rest of the screen and the undamaged unrepaired elements would demist quicker than the repaired ones.

 

A worthwhile repair though.