An ensemble of low-energy positrons injected into a supported magnetic dipole trap can remain trapped for more than a second. Trapping experiments with and without a positive magnet bias yield confinement times up to τ_{A}=(1.5±0.1) and τ_{B}=(0.28±0.04) s, respectively. Supported by single-particle simulations, we conclude that the dominant mechanism limiting the confinement in this trap is scattering off of neutrals, which can lead to both radial transport and parallel losses onto the magnet surface. These results provide encouragement for plans to confine an electron-positron plasma in a levitated dipole trap.