You said mare.
I’ve known more mares like this than any other way, lol.
Ride well and they’ll jump the moon, ride poorly and they will (hopefully gently) correct you.
I had a horse that sounds very similar. She was a horse of a lifetime for me. She won everything in the YJC classes through the 7yos and then won everything at 1.30/1.35. Then went on to win in the 1.40m, but I could feel that we were at the top of her scope. She did absolutely nothing wrong, but instead of continuing to push her until we had a wreck I opted to step her down and let her teach my teenage daughter the ropes. And she was exactly like the OP describes her horse as with my daughter (though had never stopped with me in all the years I’d had her - from 2yo until where she was at at age 10). Sit deep and commit to the fence = jump (no matter the jump, no matter the godawful distance, no matter the height). Lean forward and loosen the leg at a bad distance = stop. Always straight, always “kind”, and never what I would consider a dirty stop.
She taught my daughter so much in the 4 years she rode her, and they finished out their last year winning in the eq/medal and winning in the 1.15m jumpers. I used to joke that I “ruined” my mare by always riding “too” proactively (my tendency is always towards “over-riding” my horses). So when my daughter got on and rode super timidly it just confused her. But boy, a horse who tattles when you’re doing the wrong thing but who jumps when you do the right thing turned my daughter into a beautiful rider. What steals the confidence is the horse who stops without a reason, and I can say that knowing why the horse was stopping just helped her fix her bad habits (again, there was nothing dirty happening, so it didn’t lead to her falling off or to ugly wrecks or anything of the sort - so that’s my caveat because again, all horses are not the same!)
After that, she was leased out to another teenager who she carted around the little jumpers with great success. And then I leased her out to an adult. I would expect her to be the same as what the OP describes here. The mare knows what her job is and she knows what the rider’s job is and she has always gently enforced her boundaries.
There is no pain. The mare is not a “stopper”. IMO, there’s a huge difference between “a stopper” and a “horse who wants you to ride”.
OP - I think you have a “teacher” on your hands. If the mare jumps when you do the right thing then you have a valuable tool to help improve your riding. Stopping 3 times in 4 months is certainly not something I would worry about, and the fact that it happens regardless of the height tells me that the horse is probably legitimately confused or annoyed (again, it’s a mare 
)
Of course there are a million different things that could be going on (because…horses), and your horse may not be the same as the horse I had. But I just wanted to provide the perspective that a horse that stops the way you describe does not automatically equal a bad horse and does not mean there’s anything nefarious going on.
