I was able to catch a friend's horse who was previously only caught by using a tranq gun. I just spent quite a while scratching his itchy spots through the fence and he suddenly had an interest in people.

My hinny is extremely difficult to catch out in an open pasture. But I can open the gate and she will come out of the pasture, go into a corral and wait to be caught. That is just her routine and understanding about how to interact with people (probably her whole life was spent being roped or cornered and grabbed). I'm ok with that and she has gotten better.

She was sold to me because she was bolting away from people and short of being tied to something, her previous handler couldn't hold her when she wanted to leave. I make a genuine effort not to ever chase her and she knows it. She does like to come out and go for a ride so that is an advantage. If I'm riding another horse she is waiting by the pasture gate to come out.

Actually I have a couple with a similar history and I can catch them fine. I remember one I had to load loose into the trailer to haul home when I bought her because she just wasn't interested in being caught. I backed the trailer up to a large turnout and very slowly moved her to it, she was one to bolt like a freight train if bothered. Some horses might take more time than others to come around depending in their previous handling.

Sometimes it is easier to catch a horse by the foot or by the tail rather than the face. That is, picking up a horse's hoof and see if they will stay, or lay a rope over their back and some will just follow that rope without the halter on. (When I'm halter training an unspoiled horse unlike to just use a rope that isn't tied on and see if they can follow that for starters.)

With one of these latest difficult to catch horses, I could ask him to drop his head and just tied a bowline knot around his neck rather than halter him. He had a pretty big aversion to the crown piece on the halter and would initially get all hyped up if his head was being "trapped". He would start to get light on the forehand and think about leaving when held tight as well.

Mostly you just start with what a horse understands and then build on that. Change their expectation and work towards the response that you want, making sure they understand along the way. Can't really put a time limit on that. Usually the quickest way is to go slowly. That doesn't mean it takes forever, just means don't rush the horse.

The only horses I've met who really weren't interested in being catchable/trainable were very feral. Some may have come around with extended expert handling (if a person of such experience was willing) and some needed expert handling via a chute and were still not really safe to handle that way. With the right facilities and equipment any wild horse can be managed in theory.

"It's really quite amazing what a horse will do for you, if he only understands what you want. 
And it it's also quite amazing what a horse will do to you if he doesn't." ~ Bill Dorrance