The neutron beta-decay lifetime plays an important role both in understanding weak interactions within the framework of the Standard Model and in theoretical predictions of the primordial abundance of 4He in Big Bang Nucleosynthesis. In previous work, we successfully demonstrated the trapping of ultracold neutrons (UCN) in a conservative potential magnetic trap. A major upgrade of the apparatus is nearing completion at the National Institute of Standards and Technology Center for Neutron Research (NCNR). In our approach, a beam of 0.89 nm neutrons is incident on a superfluid 4He target within the minimum field region of an Ioffe-type magnetic trap. A fraction of the neutrons is downscattered in the helium to energies <200 neV, and those in the appropriate spin state become trapped. The inverse process is suppressed by the low phonon density of helium at temperatures less than 200 mK, allowing the neutron to travel undisturbed. When the neutron decays the energetic electron ionizes the helium, producing scintillation light that is detected using photomultiplier tubes. Statistical limitations of the previous apparatus will be alleviated by significant increases in field strength and trap volume resulting in twenty times more trapped neutrons.