I live in Texas and have this plant., mine has never had a pest problem. My tropical hibs do every once in a while. But I can usually control with soaps and horticultural oils. If the pest isn;t living on the plant, then my two cents would be maybe spray your yard (grass, trees, fence, not the plant)with one of those yard guard products. Most have permethrin which isn't too nasty...

Then try a systemic on the Texas star. (watered into soil not applied to foilage) Something with Imidacloprid as the active ingredient. Imidacloprid, while obviously not "organic" is not too nasty either. Actually, if you have dogs you may have given it to them as medicine. (K-9 advantix)

I'll prbably be chastised for reccomending chemicals....If you're not cool with that then maybe try a different plant.