We study the behaviour of the correlation robustness of two spatially isolated charge-qubits started initially with a maximally correlated nonsymmetric Bell-state. Each charged qubit is coupled individually to a superconducting resonator coherent field. The dynamics of the qubit-resonator quantum correlations, based on trace-norm measurement-induced non-locality (MIN) and Bures distance entanglement, are investigated under the effects of the qubit-resonator interactions, intrinsic decoherence, initial coherent intensity cavity as well as of the qubit-resonator detuning. It is found that the trace-norm MIN correlation can be enhanced by the initial coherent field intensity and the detuning. The MIN is more robust, against the qubit-resonator interactions and the decoherence, than the Bures distance entanglement. Furthermore, the correlation robustness analysed for the different cases of the coherent states depends not only on the intrinsic decoherence but also on the coherent states and the qubit-resonator detuning.