The inaccurate warning and inaccuracy are due to the solver called by CVX, not CVX itself. You may find that Mosek works more relaibly than SeDuMi or SDPT3, especially on numerically challenging problems, which perhaps yours is; but we won’t know until we see it.
Perhaps a forum reader can provide some assessment if you provide a complete reproducible example, to include all the input data as well as the solver and CVX output.
Aside from the differing abilities and numerical robustness of the solvers, one other possibility to consider is that you did not actually submit the same problem to mincx and CVX. In the interest of completeness, you should post your mincx code and output as well, although there may not necessarily be readers on this forum knowledegeable in mincx.