That is because CVX’s Successive Approximation method for dealing with exponential cone problems is unreliable.
if you have access to Mosek 9.2 use that as the solver. Otherwise, install CVXQUAD and its exponential.m replacement, and follow the instructions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions