How do I stop water from coming under my multitrack sliding doors?
First does the patio roof have eaves drops/gutters?  If not I would recommend installing them.  This will help divert some of the rain water away from the deck and keep water from splashing on the deck. If you still get a lot of water at your door after the eaves drop/gutters you can then try one of the following:

1) Re-grade the deck away from the doors (as Tester101 suggested in the comments). This would be the best solution.
2) Install a trench drain system (flush with the deck) to divert water away from the door.   Some issues with would be making sure the locations of drains catch and divert the water away from the doors.


3) Use a leaker blocker dike (http://www.newpig.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10651&amp;catalogId=13007&amp;productId=141454&amp;langId=-1&amp;cm_vc=vc_fast_finder) to divert the water away from the door.  Some issues with this method would be installing it before it rains, slight leakage between the dike and floor, installing in the correct location to divert the rain, and getting rid of the water after the rain.