You haven’t shown is the output. You haven’t shown us on what iteration the solution becomes unbounded (if that is indeed the nature of the “failure”).
I don’t know whether this SCA is appropriately bounded to prevent unbounded subproblems, but nevertheless, SCA can be very precarious, unreliable, and non-robust. NaN——Status: Infeasible Optimal value (cvx-optval): - Inf - #2 by Mark_L_Stone
Moreover, I have no idea whether you have correctly implemented the algorithm in the paper. Your code is rather complicated and I don’t know whether it is 'correct", but I wouldn’t be surprised f it is not. Even if it correctly implements the algorithm in the paper, it might not work for all starting values, input data, choice of solver, or whatever.