Dynamic SABR layer-by-layer calibration fails at third layer: implementation issue or no admissible solution?

I am implementing the layer-by-layer calibration of the time-dependent SABR model described in Hagan, Lesniewski and Woodward, Managing Vol Surfaces . In particular, I am using the effective-parameter formulas around equations (3.7)–(3.8) and the piecewise-constant integral update formulas in equation (3.11) of the paper. For each expiry $T_j$ , I first calibrate a standard SABR smile and obtain target effective SABR parameters $$ (\alpha_j^, \rho_j^, \nu_j^*).