An unexplained >4σ discrepancy persists between "beam" and "bottle" measurements of the neutron lifetime. A new model proposed that conversions of neutrons n into mirror neutrons n^{'}, part of a dark mirror sector, can increase the apparent neutron lifetime by 1% via a small mass splitting Δm between n and n^{'} inside the 4.6 T magnetic field of the National Institute of Standards and Technology Beam Lifetime experiment. A search for neutron conversions in a 6.6 T magnetic field was performed at the Spallation Neutron Source which excludes this explanation for the neutron lifetime discrepancy.