What do you mean by only having one wire on your fence exactly? If you mean you have run hot wire around a wood or high tensile fence then yes, one wire should suffice. But if you mean there is only one wire between your horse and total freedom then I would recommend adding one if not more strands, for your horses safety and that of anyone who could get hurt should your horse get out, especially if you are having issues with him touching it and not getting shocked.
One wire is plenty if the fence is working.
Several things can cause your fence not to be working, here's some things to check.
-Bad ground as already discussed.
-Grass, limbs, snow or anything else that is touching your fence will ground it out. Walk your fence and make sure absolutely nothing is touching the wire but insulators.
-Insulators that are dirty, snow covered, draped in spider webs or anything else that can cause a path from your wire to pole can cause a fence to ground out. While walking the fence looking for above, check each and every insulator too. Keep a few in your pocket as a just in case, beats treking back to the barn for supplies. Experience has taught me that if a insulator starts to get cracks in it from the sun it's time to change it as it will be causing problems shortly if not already.
-Bad charger is not uncommon and just because the light is blinking doesn't mean it's working. Get a tester (or be brave and use your finger), disconnect the hot wire (leave ground on) and test right there. If it's hot your charger is good, if not there's your problem.
-If everything checks yet you are still having problems you'll have to break your fence down into sections by snipping the wire (I usually do this at the corners but anywhere is good). Hook one section up at a time starting closest to your charger and using your fence tester. When it goes from good to bad you now know in what section you are having problems. What I've found doing this is mostly it is caused by a bad insulator or two. Couple times it was caused by old steel wire that was corroded.