Why do they stop? We are glad you asked, it is because that's their natural reaction to a worrisome or unpleasant situation. Even nervous and timid horses will stake themselves to the ground because they are very apprehensive about leaving the herd or the barn where they feel protected and safe.
What other reasons are there for napping? One is the horse just isnt sure what to do. They'd rather stop or stand still than move forward. If your horse naps in a place he's familiar with (ie. your home area) then you should check your tack for things like a poorly fitted saddle. The pain could become unbearable and at that point the horse simply won't move.
Often, a horse will react to bad fitting tack by rearing or even bucking. So when tack is bad fitting, napping is a pretty good alternative.
A secret tip about nappers is to closely observe where they're napping. If you find they get nappy around certain things or places then you might be able to spot a pattern. For instance, if every time your horse rides by a tarp and he stops, that is likely your culprit. But it could be lots of different things. It could be bushes. Trees. Dog pens. Or anything really.
What should you do while you're patiently waiting for your horse to move? If you're with friends it may be a good idea to warn them before hand that this may happen. You may have to sit there and have a conversation. If you're by yourself bring a crossword puzzle or maybe even a book. Do whatever it takes for you to pass the time and do not get impatient.
Just remember to treat the situation as you would a horse that's spooking. Most of the time, napping is a reaction to spooking. You simply have to be patient and wait it out.