CVX status failed after the status is solved

What may be the reason for getting Nan

CVX’s Successive Approximation method was invoked to deal with functions which invoke the exponential cone. It is an unreliable method, and has been superseded by Mosek, which has a native exponential cone capability, or if that is not available, CVXQUAD.

If you have access to Mosek, use it as solver. Otherwise, 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

It may or may not also the case that the input data your problem is badly scaled, i.e., non-zero numbers which are not within a small number of orders of magnitude of one. If so, that is bad no matter what solver or solution method is used.