  We derive sufficient conditions for infinite-dimensional systems whose
entanglement is not completely lost in a finite time during its decoherence by
a passive interaction with local vacuum environments. The sufficient conditions
allow us to clarify a class of bipartite entangled states which preserve their
entanglement or, in other words, are tolerant against decoherence in a vacuum.
We also discuss such a class for entangled qubits.
