It is the same reason that all your speeds change with an increase in altitude. Density, mass flow etc. You just need more speed to achieve the same mass flow and get sufficient bernoulis across your wing.
You need to find a set of APTL notes on performance from a while ago which include the D&X calculations from first priciples. Sorry don't have any to hand but some descent chap who flew in the days of comets etc might be able to help you.