The speed of the motor is determined by resistors in the switch. A dry windshield will increase the load and couple that with the reduction of power and maybe even a low battery and voila, you have wipers that stop where they shouldn't.

1) try the switch in all speeds
2) disconnect the linkage and see if its still a problem

Oh, here's something to check ... when the wipers stop, is the motor still turning? If so, the big gear in the transmission has stripped teeth.