The UCNτ experiment is designed to measure the lifetime τn of the free neutron by trapping ultracold neutrons (UCN) in a magneto-gravitational trap. An asymmetric bowl-shaped NdFeB magnet Halbach array confines low-field-seeking UCN within the apparatus, and a set of electromagnetic coils in a toroidal geometry provide a background "holding" field to eliminate depolarization-induced UCN loss caused by magnetic field nodes. We present a measurement of the storage time τstore of the trap by storing UCN for various times, and counting the survivors. The data are consistent with a single exponential decay, and we find τstore = 860 ± 19 s: within 1σ of current global averages for τn. The storage time with the holding field deactiveated is found to be τstore = 470 ± 160 s; this decreased storage time is due to the loss of UCN which undergo Majorana spin-flips while being stored. We discuss plans to increase the statistical sensitivity of the measurement and investigate potential systematic effects.