Why will he not stop and ask for directions? Because he is a man.
The main reason men do not like asking for directions is because they have a strong belief that they can do it on their own.
If they are lost, they will be able to find their own way out, on their own, without needing help from anyone.
Where women are willing to ask for and receive help from anyone (even gas station clerks), men feel their intellect is being challenged if they have to ask for help.
Men associate their value as a person with their ability to figure things out on their own.
From The Guy Rules: Christopher Columbus did NOT need directions and neither do we.
Men: When you are with a woman and she suggests you ask for directions, do not think of it as an insult.
Think of it as another way you can make her happy.
You will be getting the directions just to make her happy, and not because you could not figure it out on your own.
Women: Next time you are with a man and you are lost, stay calm and try not to offer advice.
Try to relax and enjoy the scenery.
Give him a chance to figure it out on his own (you could even give him support with this).
If that does not work, ask him if he would be willing to stop so you can go in and get the directions.
Whatever you do, do not make him feel bad that you are lost.