In single-bubble sonoluminescence (SBSL) microbubbles are trapped in a standing sound wave, typically in water or water-glycerol mixtures. However, in viscous liquids such as glycol, methylformamide, or sulphuric acid it is not possible to trap the bubble in a stable position. This is very peculiar as larger viscosity normally stabilizes the dynamics. Suslick and co-workers call this new mysterious state of SBSL “moving-SBSL.” We identify the history force (a force nonlocal in time) as the origin of this destabilization and show that the instability is parametric. A force balance model quantitatively accounts for the observed quasiperiodic bubble trajectories.