It could be that the bit you are using is causing him some discomfort or he may just really hate the bit and therefore will not respond to any pressure in his mouth (I'd get his teeth checked). Unsurprisingly my mare hates the bit - I wouldn't want a cold metal bar in my mouth either, so we ride bitless and she responds so much better! I'd give bitless a try if I were you!
Another problem could be that you're releasing the pressure too quickly. For example, when you ask him to stop by pulling on the reins and he doesn't stop or slow down, you give up and stop pulling on the reins so he learns that if he continues walking the pressure in his mouth will go away.
Next time you ask him to slow or stop, keep pulling and slowly increase the pressure until he slows and stops. Reward every correct action he does by releasing the pressure.
It's useful to have a verbal cue to stand which you can teach your horse on the ground and practice through groundwork before trying it on his back.
Hope this helps :)
I've also had this problem. If your horse doesn't stop on command try facing him/her towards a wall since he/she won't be able to go forward into the wall. Practice this a few times and make sure that your aids like sitting deep in the saddle, leaning back a bit, and some outside reign are very clear. Hope this helps!
Hello Della. I've had a similar problem in the past. When I asked my horse to stop, I'd use my seat. If your horse doesn't stop immediately after you ask him too, back up. Then als for the stop again. Keep backing up until he stops when you want him too. Hope this helps.