OK I have a few things to address here.
#1 is that 14 years old is not old. That's when they are seasoned and just getting good. That's middle age.
#2 You didn't say why he isn't doing well at shows anymore. Do you mean he is ring sour, or that the judges just are not placing him anymore?
If the latter is the case, then adjust his classes to something he will still get looked at.
#3 He could very much be missing his child. But also, I see a depression that could also be caused by any number of other underlying causes.
A horse that is depressed should be first and foremost examined by your vet to rule out anything physical.
I'm thinking pain is involved someplace because there is a reason that he is not wanting to move.
He is hold up in that stall for a reason so let's rule somethings out:
He could be standing in that stall because he's cold for one thing. Have you really felt him? Is he cold or clamy to the touch? Does he have ample feed and hay in front of him to keep him warm and warm water? If it's windy, they hate that. They can get earaches from having to stand in the wind.
Let's discuss artheritis.
People are under the impression that horses don't have it, unless they display outward symptoms. Wrong. Just because he is not limping or snapping or clicking any ligaments, does not mean that he is pain free. Especially if he was used for any performance events in the past. I'd have him on something for that. Maybe he doesn't want to move and go romping because he's stiff or in pain. It does not have to be in his legs. It can be anywhere, shoulders, hips, back.......etc.
Now there's his mind.
He maybe in great need of a mental tidy.
Some horses just hate it when they loose their job. Some horses thrive on working and will give you their heart and simply cannot bear it when they are retired and "out to pasture" so to speak and will sink into depression. They don't like feeling useless.
Then we have the weather. The weather especially the winter weather blahs can be affecting him. Just ask me. I've got houseatosis big time here. Glummy days, Christmas is gone, and spring is not in the air. Bummer.
The other thing that is bothering me is that he seems to have changed hands a lot. I wonder how many homes he has had. I really hate that with a passion, horses being passed around every couple of years. So not fair. People just don't seem to get it that horses are living, breathing, heart beating animals with feelings and they just pass them around like nobody's business left and right for whatever reason. Not saying that this is the fact because I don't know, but I'm just laying this out there for consideration too. He simply might be sick and tired of constant changes in his life and loosing his child might have been the breaking point for him.
You have stated that you don't have much time for him anymore, but would like to keep him. Well.......that would be nice if he were happy but it doesn't appear that he is.
So what can you do?
I'd start to put a plan in place. I would start with a good exam by the vet to rule out any pain problems or health matters. If he comes up clean as a whistle, then that means it's mental. You should do for him what you think he wants, and what will make him happy again. Just think about it. When and where was the last time you really saw that he was happy? And go from there.