  We introduce an arbitrary number of accessible modes when analyzing bipartite
entanglement degradation due to Unruh effect between two partners Alice and
Rob. Under the single mode approximation (SMA) a fermion field only had a few
accessible levels due to Pauli exclusion principle, conversely to bosonic
fields which had an infinite number of excitable levels. This was argued to
justify entanglement survival in the fermionic case in the SMA infinite
acceleration limit. Here we relax SMA. Hence, an infinite number of modes are
excited as the observer Rob accelerates, even for a fermion field. We will
prove that, despite this analogy with the bosonic case, entanglement loss is
limited. We will show that this comes from fermionic statistics through the
characteristic structure it imposes on the infinite dimensional density matrix
for Rob. Surprisingly, the surviving entanglement is independent of the
specific maximally entangled state chosen, the kind of fermionic field
analyzed, and the number of accessible modes considered. We shall discuss
whether this surviving entanglement goes beyond the purely statistical
correlations, giving insight concerning the black hole information paradox.
