This problem is fuel starvation caused by fuel sloshing around in the tank during hard cornering. Depending on the direction of the turn, the fuel pump pickup can get uncovered, leaving the pump with nothing to pump but air.
Owing to differences in fuel tank design, 1G AWDs have this problem when executing hard left corners, while 2G FWD turbos have problems with hairpin right turns. In both cases the fuel pickups are on the side of the car which is on the inside of the turn; of course, the fuel wants to be on the outside (opposite) side of the car.
The only fix for this problem is to have enough fuel. Most recommend at least 1/4 tank of fuel, but some hardcore autoxers say they need at least 3/4 of a tank.
2G AWDs and 1G FWDs apparantly do not suffer from this problem as much, as their fuel pickups are located differently. Despite this, autocrossers may still run into the problem.