Your CVX code models X1/max(1+X2,0)
That is neither convex nor concave.

For X2 > -1, this simplifies to X1/(1+X2). Now restrict this to X1 and X2 are positive. Evaluating the Hessian of this at X1 = X2 = 1 produces one positive eigenvalue and one negative eigenvalue. So neither convex nor concave even on this restricted domain.

That function is not concave. The subject of what would be a good approximation for your purposes is outside the scope of this forum. If that is really the function you wish to maximize, you may be better off using a non-convex solver.