It is a little hard to say what is going on without much information. What does the texture mapping in Rhino viewport look like, and what kind of map are you using?
I do not know if the problem stems from the fact that an object is modeled with tspline .. it seems that once he takes ultimate deformations and folds in memory of the solid edges early ... so when she got there the texture does not continue ..
Intel Core i7 950\Zotac ION 512 mb, 1 Gainward 780 ti 3 gb\ 12 gb\ W7