Alex'x analogy to driving made me remember that my old instructor used to make me think of cantering as changing gears. She would have me rev the horse up a bit, but not let it go forward, as a person would do in driving a stickshift, reve the engine and then pop the clutch. But in any case, this analgoy might be meaningless to you.
So, as far as keeping the horse cantering once it has started:
Yes, you may need to put some leg on. Think of it more as "confirming" that canter is correct. As you go along, if you feel the horse is about ready to drop out of the canter (and it takes awhile to learn to feel this) you put your leg on and kind of squeeze a bit, just enough to say "yes, that's right, canter on".
The horse may break out of the cante because it senses that yoiu are not well balanced or that you are locking up your body. A stiff body is basically a sign for a horse to come to a stop, so it will help you to keep him going forward if you can learn to be relaxed and move with his body.
You see, this is a lot to learn, isn't it? It really takes time. It is easier, perhaps, to canter on a horse out in a field, following another horse. And I would certainly encourage you to have more such experiences. But you will find that riding in the arena, where you are learning to not only sit the canter, but eventually to effect it, is much harder.
Your frustration is quite normal, and I would just try to accept that it will take time to learn to canter. In the Spanish riding school of Dressage (where you have the famous Lippizan Stallions) the riders must ride for TWO YEARS! On a lungeline. How about that!
Personally, I think you should be glad to do lungeline lessons while you have them.