You know the quotation. It's from Winston Churchill, Britain's great wartime leader. "Never give up. Never, never, give up." It's tossed about in the horse world as much as in any other field of endeavor, and when it is, the message is clear: Keep going. Don't be a quitter. Never give up on yourself or your horse.
But Churchill's quote had a second part to it, one that's generally overlooked and which changes his meaning significantly. Here it is: "Never give in except to convictions of honor and good sense."
So what he was really saying is: Give it all you've got, be determined, stick with it--but be smart, too. If honor or good sense says you must give in, then give in you must.
That's a much different message. In the horse world, it applies most urgently when you're concerned for your safety. If you're routinely worried that you might get hurt riding or handling your horse, you must give in and listen to your common sense. If there's a serious mismatch between your horse's need for corrective training and your ability to provide it, you must give in and find a solution.
When you're in over your head, just "sticking with it" can literally be dangerous. So by all means give in and consult with a professional trainer to devise a safer and more realistic plan. It might include some professional training for your horse, and/or some training for you in the form of clinics or lessons. (And if what you need is help overcoming fear of riding, click here.)
The pro might advise you instead that letting your horse go--to someone who's up for the challenge of dealing with him--is your best option. This then frees you to find a more suitable match for yourself.
Though this can seem like "giving up," in reality it's just using common sense to provide a better outcome for yourself and your horse.
And that's a good thing.