A previously developed real-space renormalization-group approach to critical dynamics is examined. A correction to the formalism has to be introduced. The need for this correction is demonstrated through an exactly soluble one-dimensional Ising model. The new version imposes additional serious limitations on the usefulness of the method within standard approximation schemes. The second-order cumulant approximation of the two-dimensional kinetic Ising model on a triangular lattice is used to demonstrate these limitations.