Why do helicopters have a difficult time flying at altitudes above 6000 m?

A helicopter blade works the same way as a wing on a fixed wing aircraft. The air flowing faster over the top of the airfoil generates lift. When a helicopter flies at a high altitude the air gets thinner. Because the air is thinner, more pitch on the blades is needed to keep the helicopter in the air. When too much pitch is on the blades the blades stall, air moves past the bottom of the blade and creates a vortex behind the top of the blade. All lift is lost and you lose altitude.