The approach I suggested above would allow this to be done, even though it is a kluge, and requires repetitious problem solving.
First solve the original problem and record the number of iterations, say M. Then re-run CVX limiting the maximum number of iterations the solver is allowed.
for i = 1:M-1
variable x(n) complex;
A*x == y;
cvx_solver_settings('maxiter',i) % or cvx_solver_settings('maxit',i) or whatever is needed for your solver
disp([i norm(x,1) norm(y-A*x)]) % and/or save into an array, or whatever you want