An analytical solution of the dynamical evolution of two qubits confined in a transmission line cavity is obtained in dispersive limit under intrinsic noise. The dynamics of non-classical correlations are investigated by using different measures based on the skew information quantifiers [including local quantum uncertainty and uncertainty-induced non-locality], the Bell function and logarithmic negativity for experimentally chosen parameters. It is found that the generation of the non-classical correlations and its robustness depend crucially on the transverse exchange interaction, the dissipation rate, the mean photon number, and the frequency shift. The phenomena of sudden disappearance and sudden appearance of entanglement are observed. The stationary correlations appear due to the intrinsic decoherence, which depends on the parameters of the chosen initial states.