A hores has a natural walk rythm and some are slower than others. Question: Does he walk faster back TO the barn? Will he walk fast out in the pasture if you call supper time? Can he walk faster saddleless? Could be the saddle is really crimping his shoulders.
However, if he WILL walk out on the way home , then you know it's a matter of him just zoning out. Then you must get after him and really wake him up. Be sure you don't snag him in the mouth when he does wake up and move out.
Tap him , kick him and crack him with the crop. He is blowing you off, and you need to make an impression that will last, not just for two minutes. Next time , all you need to do is kick lightly and raise the crop where he can see it. But when you wake him up, if he trots or canters off, don't pull him back. Let him go and let him come back to a walk on his own.
Shoein him may make a huge difference. He might be ouchy.