All horses handlers should be able to catch horses easily. This is particularly true when you suspect that your horse has a health-related problem, and you need to catch them for examination or treatment.
Horses that run away when approached have been taught that this is a productive behavior. The cost of being caught has exceeded the cost of evading. The benefit of evading has exceeded the benefit of being caught. These associations must be changed in order for a horse to want to be caught.
I do not believe in catching horses with feed or treats. Rather, I use pressure and release.
When the horse walks away, I recommend you apply pressure by walking towards the hindquarters and not allowing the horse to rest.
When the horse moves the hindquarters away and faces you, or takes a step towards you, immediately release by standing still, or even withdrawing slightly and lowering your profile. You need to act in the split second, quickly changing your posture and presence, a skill that takes time to learn.
When working with a horse that is difficult to catch, I try to walk up to the horse regularly, apply pressure to his hindquarters until he faces me and seems to relax by chewing or sighing. I then approach him, rub his face or muzzle, or scratch his back, let him relax, then walk away without actually haltering him. I do this frequently, several times per week paying attention to the details of the interaction each time. This breaks out the "approach" and the join-up from the actual haltering, which is important.
When clients talk to me about these kinds of behavioral and training questions, I usually try to put them in touch with a qualified trainer. I have a particular interest in solving these kinds of behavioral problems but often will not be the one to work with the horse directly if there is a qualified trainer available to help.
In my opinion that these sorts of skills are foundational. If you are achieving great things in your riding but are struggling with the basics of loading, tying, catching, then you are missing a vital and important piece of the relationship with your horse. My advice to you is to seek to change that. Every horse should be easy to catch.
Tips for safety & Success
This is not an easy skill to describe. Your ability to catch a horse is related to your ability to get a horse to do many other things. If you lack confidence, skill or good timing, catching them may be difficult.
Set yourself up for success by putting the horse in a location in which there are not excessive obstacles like trees to complicate the interaction.
Practice this skill when you do not need to catch your horse, and when you have the time and patience to do it right. The time to teach a horse to be willingly caught is not when you need to catch them.
Improvement can be reinforced by keeping your horse alone in a moderate-sized corral. It can be hard or impossible to teach your horse to be caught easily when kept in a group of other horses or in a large turnout area with trees and other physical barriers.