  We study a generalized double Jaynes-Cummings (JC) model where two entangled
pairs of two-level atoms interact indirectly.
  We focus on the case where the cavities and the entangled pairs are
uncorrelated. We show that there exist initial states of the qubit system so
that two entangled pairs are available at all times. In particular, the minimum
entanglement in the pairs as a function of the initial state is studied.
Finally, we extend our findings to a model consisting of multi-mode atom-cavity
interactions. We use a non-Markovian quantum state diffusion (QSD) equation to
obtain the steady-state density matrix for the qubits. We show that the
multi-mode model also displays dynamical preservation of entanglement.
