We evaluate the dynamics of quantum and classical correlations in the presence of non-Markovian noises.By considering an entangled pair of spins in the noise environment described by Ostein-Uhlenbeck processes, we show that the quantum discord of some states is completely unaffected by independent Ostein-Uhlenbeck noises for long intervals of time, and that the inevitable onset of the sudden decrease of the quantum discord can be substantially delayed by the decrease of the noise bandwidth γ, where γ = τ defines the environments finite correlation time of the noise.