We present a localized solution to the problem of entanglement degradation in noninertial frames. A two-mode squeezed state is considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated), each observing a single localized mode of the field. We study the state of these modes to determine how much entanglement the observers can extract from the initial state. The dominant source of degradation is an inevitable mode mismatch between the mode of the squeezed state Rob is given and the mode he is able to observe from his accelerated frame. Leakage of the initial mode through Rob's horizon places a limit on his ability to fully measure the state, leading to an inevitable degradation of entanglement that even in principle cannot be fully retrieved by any measurement device.