We describe a model for the long term evolution of a circumplanetary disk that is fed mass from a circumstellar disk and contains regions of low turbulence (dead zones). We show that such disks can be subject to accretion driven outbursts, analogous to outbursts previously modeled in the context of circumstellar disks to explain FU Ori phenomena. Circumplanetary disks around a proto-Jupiter can undergo outbursts for infall accretion rates onto the disks in the range ~10^{-9} to 10^{-7} M_sun/yr, typical of accretion rates in the T Tauri phase. During outbursts, the accretion rate and disk luminosity increases by several orders of magnitude. Most of the planet mass growth during planetary gas accretion may occur via disk outbursts involving gas that is considerably hotter than predicted by steady state models. For low infall accretion rates less than ~10^{-10} M_sun/yr that occur in late stages of disk accretion, disk outbursts are unlikely to occur, even if dead zones are present. Such conditions are favorable for the formation of icy satellites.