We study the influence of atom-surface interactions close to the surface on the confinement properties in a recently proposed model [A. Jurisch and H. Friedrich, Phys. Lett. A 349, 230 (2006)] for quantum reflection traps and test the reliability of the sharp-step approximation used there. Accurate numerical calculations show a dependence of the surviving particle fraction on characteristic potential lengths determined by the behavior of the interaction in the limits $r\ensuremath{\rightarrow}0$ and $r\ensuremath{\rightarrow}\ensuremath{\infty}$ of the atom-surface distance $r$. For interactions dominated by the retarded potential proportional to $1∕{r}^{4}$ we find that the simplified sharp-step potential reproduces the behavior of the trapped atoms well, both qualitatively and quantitatively.