If you have access to Mosek 9.x, use CVX 2.2, with Mosek as solver.
Otherwise, follow the advice 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
However, if you are solving a sequence of CVX problems as part of Successive Convex Approximation (SCA), it may that your overall SCA algorithm is unstable and diverges, thereby creating more difficult to solve CVX problems. If you follow the advice in the link, you may or may not succeed in soving all the CVX problems You might be better off using a non-convex solver available under YALMIP than using SCA if your name doesn’t happen to be Stephen Boyd, which it’s not.