Agree with a lot of what NM has said. Also agree that it depends what I see/get at any given time as to what exactly I'd do. Also depends a bit on the horse's innate personality. We need more info for anything more than generic advice tho.
What do you think happened to make her change her behaviour? What has been happening in the past few weeks/months? What is your routine with her? What do you generally do when you get to her?
If there's nothing at all obvious that stands out in the recent past, I'd guess that she's had a bad fright from someone else & is now skeptical about people generally. Or perhaps you unknowingly hurt her - or she got herself hurt - last time you had her, which she's associated with you. Perhaps she's in season or otherwise hurting anyway & doesn't trust or want anyone to touch her ATM. Or perhaps due to what you've been doing with her, she's been gradually getting more skeptical, less friendly, but you didn't notice until she refused to be caught any more.
Considering the above, you may guess that I disagree with NM that it is purely or otherwise 'misbehaviour' or 'respect'. Or perhaps more accurately to clarify, I really mean that whatever the cause, it IS always 'misbehaviour' and lack of respect or trust in you. However, I don't think these lables are helpful, and they often lead to the wrong attitude on behalf of the trainer, IME. Whether or not you discover the actual cause, I think it's important to learn to understand & see her point of view, and convince her, in a considerate manner that it is actually in her best interests to come when called.
I also basically agree with & use the tactics NM has suggested. I find your suggestion about 'uncertain' horses & your 'stubbornness' a bit ambiguous tho NM, so will endeavour to clarify what *I* think & do on that note.
I agree that by all means, taking however long it takes without getting impatient, giving up or trying to force the issue is important. But this doesn't mean you have to get the whole job accomplished in one session. Actually think it's generally better not to, but to work in short, easy sessions & accomplish small 'win/wins' along the way. Generally it works out that I can accomplish a LOT more with a horse for every hour spent, if I do it in lots of small, easy sessions with stress-free breaks in between, than if I were to do it in a few longer sessions. Sometimes 10 minutes is too long a session for that horse, that task at that time. It's what's happening at the time you quit(what behaviour or attitude you're negatively reinforcing), not whether you quit before accomplishing your goal.
Eg. If the horse stands an looks at you, but gets antsy when you focus on her or approach her, I'd be asking for her to accept *just a tad* past her comfort zone for the moment. Eg. I'd take only one step towards her and then turn & walk a few paces back. I'd repeat this until she wasn't so uncomfortable with it, before going a few steps at a time. I would strive to be attentive to her enough that I was turning away *before* she felt the need to do so herself. This is gaining her trust, that you're not just going to push blindly through barriers and force her into situations she's not able to give. That you respect her, which is, I feel, the start of gaining respect from her.
BUT if/when she did turn away, then I'd put *a little* pressure on her - wave a stick/rope gently at her rump, walk calmly after her. Continue to do this until she gives the smallest sign she is willing to try something else other than leaving - even if it's a momentary look or hesitation. At that instant, I'd turn away & stand relaxed for a minute, before either quitting the game for the time being or attempting to start approaching her where I left off.... or with a little less pressure to begin again.
Once I got to the point where the horse was allowing me to walk up, or coming to me, I'd be ready with positive reinforcement - likely Something Yummy(because they're still probably too skeptical for anything else like a neck rub to be desirable) and negative reinforcement - remove the pressure by walking away immediately the treat's given. I wouldn't attempt to touch, let alone halter the horse until she was confident just being close to me.