Measurements of the lifetime of neutrons trapped in a bottle have been consistently shorter than the lifetime measured in neutron beam experiments. With trapping potentials as low as 50 neV and neutron detectors located only at the top of the bottle, this discrepancy could be the result of the soft scattering of dark matter with neutrons. However, it is challenging to obtain the observed loss rate in conventional models of dark matter scattering. We show that this phenomenology is possible in composite models of dark matter where the soft scattering is from dark matter that has been captured and accumulated in the earth. This solution can be tested by placing more neutron detectors around the trap, providing better angular coverage. The phenomenology of soft scattering by trapped composite dark matter is generic and suggests new experimental directions that could be pursued to detect this large class of models.
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