dig around the patio and force the water to move to both/either side of the slab.
I did that to the end of my property which was draining into a neighbors yard and flooding their basement. It's been working for about 15 years now.
My brother had a similar problem with being about 3 feet below road level, he just dug the trench (only about 7 or 8 inches deep) and directed the water away.
It may fill up with leaves and debris and need to be dug out in a couple of years but it's not a big deal. A spade and some elbow grease and you potentially could be just fine.