What would be a good ground cover or gr to plant in a semi-shaded area with high traffic in SW Florida?

We have an area on the side of our house that is shaded by my neighbor's 30'-40' wall of Areca palms . We have sodded three times there already with Fortran sod, but it always dies. The only thing that seems to grow there, besides a couple papaya trees & other shrubs, is weeds. I am tired of sodding that area only to find that it always dies. What else can I do?