Post a picture of the outside.
Hard to know what your talking without one.
Slab stick out beyond the bottom plate?
No gutters?
Wall not at least 6" above grade?
Any of these will cause an issue.

 

You'll never stop it all as rain can go horizontal in a strong wind.
I assume you don't get snow?

Pictures as Joe asked.

Bud

 

Pics would be nice but I'm not sure there is a solution short of closing it in [walls/windows] Screening it in would help some.

 

Open patio must be built so no water can rot the parts (esp floor - tile on slab, eg). Don't know if you'll like the look but you can install roll up screens (synthe bamboo looking) outside which should limit the water coming in. If too wide openings, screens can become heavy. Homedepot screens are bound to fail early, esp any hardware.

My plan (if deck turns into a roofed patio) is to have partial glass wall, using existing storm windows (when windows are replaced) and looking for used sliders for cheap.