We address the dynamics of a two-qubit system interacting with a classical dephasing environment driven by a Gaussian stochastic process. Upon introducing the concept of entanglement-preserving time, we compare the degrading effects of different environments, e.g. those described by Ornstein-Uhlenbeck or fractional noise. In particular, we consider pure Bell states and mixtures of Bell states and study the typical values of the entanglement-preserving time for both independent and common environments. We found that engineering environments towards fractional Gaussian noise is useful to preserve entanglement as well as to improve its robustness against noise. We also address entanglement sudden death by studying the entanglement-survival time as a function of the initial negativity. We found that: i) the survival time is bounded from below by an increasing function of the initial negativity, ii) the survival time depends only slightly on the process used to describe the environment and exhibits typicality. Overall, our results show that engineering the environment has only a slight influence over the entanglement-survival time, i.e. the occurence of entanglement sudden-death, while it represents a valuable resource to increase the entanglement-preserving time, i.e. to maintain entanglement closer to the initial level for a longer interaction time.