We investigate the effect of mass loss on the invariants of single particle motion in potentials having translational or rotational symmetry. These systems are non-Hamiltonian in the physical momenta, but for non-velocity-dependent potentials can be made formally Hamiltonian by treating the velocities as canonical momenta. Applying Noether's theorem to the formal Hamiltonian then yields global invariants corresponding to its symmetries. For velocity-dependent potentials, an exact invariant is constructed from the (non-Hamiltonian) vector field. The results are applied to charged particle motion in a magnetic dipole and agree well with numerical calculations.