In a highly polarized liquid (laser-polarized 3He-4He mixtures in our experiment), dipolar magnetic interactions within the liquid introduce a significant nonlinear and nonlocal contribution to the Bloch equation that leads to instabilities during NMR evolution. We have launched a study of these instabilities using spin echo techniques. At high magnetizations, a simple 180 degree rf pulse fails to refocus magnetization, so we use a standard solid-state NMR pulse sequence: the magic sandwich. We report an experimental and numerical investigation of the effect of this sequence on unstable NMR evolution. Using a series of repeated magic sandwich sequences, the transverse magnetization lifetime can be increased by up to three orders of magnitude.