We study experimentally the stability of excited, interacting states of bosons in a double-well optical lattice in regimes where the nonlinear interactions are expected to induce "swallowtail" looped band structure. A dynamic homogeneous Gross-Pitaevskii calculation indicates that the double-well lattice both stabilizes the looped band structure and allows for dynamic preparation of different initial states, including states within the loop structure. The homogeneous calculation predicts that the loop states, unlike the ground states, should be dynamically stable. An inhomogeneous mean-field calculation including the trap potential, however, implies that the decay is dominated by inhomogeneous effects and that there is little variation in the decay rate among the states prepared within the loop structure. By experimentally preparing different initial coherent states and observing their subsequent decay, we observe distinct decay rates in regimes where multivalued looped band structure is expected, although not the stability predicted by the homogeneous calculation.