In reply to Chris Huntington:
Due to the prevailing wind at the midi, its more direction, rather than actual speed that closes the lift, thankfully its more likely to be shut down by lighting risk than the wind. But going back to your question, not sure of the speed that is needed to close the lift, but that's why the midi arête can be a total wind fest, but the cable car still functions.
As for the Flegere, its invariably the foen wind that is channelled down the Mer de Glace that causes the problem there, the area is known for being the windiest in the valley during these periods.