Okay... she DOES canter... it's not that she's refusing to canter, just that before she goes into, and as she's coming down from, she gaits. There are other times when she gaits instead of cantering - but those times I can see that the rider didn't set her up right.
She is trimmed by a Saddlebred enthusiast. She gets a balanced, barefoot trim suited to her and her conformation. She has GREAT feet, and tends to wear on her own, needing little in the way of trimming.
She has not been checked by a chiropractor - I can't get one to my area at the moment, but am trying (also trying equine physios, massage therapists etc. ) to get one who will travel to me. (I live out of the way, in a small community - many professionals won't come unless we have 5 or more horses to work on). I suspect there is some back pain, likely around the SI joint, she doesn't give anything away obviously (and I have only had her a few months) but there's just a feeling I get watching her that she finds it difficult. I have talked with a human physio - and she explained that without the muscle tone to hold the SI joint stable it's very likely she's got a little bit of pain due to the joint(s) not having enough support. She did give us some things to work on to help work those muscles, but I'm still going to try and get someone out to have a look.
When asked to canter she tends to bring her head up, hollow her back... and then the footfalls change from a trot to an ugly four beated thing (with feet flying everywhere) for a few strides then she'll go into the canter and sort herself out. Once in the canter she seems happy enough to stay in it... but that break in stride has been a frustration on the dressage and hunter standpoint. Coming down goes much the same way, but not as often (it doesn't happen every time)
In the field she can and does canter, it's not always pretty or balanced, she definitely prefers the trot (and man can she trot!) possibly because she doesn't like to be left behind and her canter/gallop is very slow. Under saddle her canter tends to be more balanced, providing the rider does their part in keeping her balanced.
She was out of shape - as in not a bit of muscle beyond what she needed to walk around a small paddock. She has been brought up, slowly, so that she has some muscle, but looking at her she still looks unfit (unlike my other two saddlebreds she has no real "tone" to her...) and has little in the way of a topline (the lack of topline is the second reason I suspect there may be some discomfort or pain of the back.. she really resists using herself correctly and therefore isn't building up those muscles).
I hope I got everything?