We describe a family of posets with positive flag $h$-vectors that do not admit an $R$-labeling. This family contains the example of R. Ehrenborg and M. Readdy presented in [4]. Furthermore, for a poset that has an $R$-labeling, we consider the complex of all rising chains. We show that the $f$-vector and homotopy type of this complex do not depend of a concrete labeling.