No. As long as the car is in their lot, which is their private property, they do not have to care how far you drive.
Simple solution: Start your own business and make your own rules.
If that's a simple solution, I'd sure hate to see a complicated solution.
Did it!
The problem with your argument is the protection of the constitution and certain rights such as the right to bear arms. The employer and property owner has a right to excersize certain positions but not to violate rights. Try and tell someone who is a minority race you don't want them in your parking lot.