Nanocrystal quantum dots are attractive materials for applications as nanoscale light sources. One impediment to these applications is fluctuations of single-dot emission intensity, known as blinking. Recent progress in colloidal synthesis has produced nonblinking nanocrystals; however, the physics underlying blinking suppression remains unclear. Here we find that ultra-thick-shell CdSe/CdS nanocrystals can exhibit pronounced fluctuations in the emission lifetimes (lifetime blinking), despite stable nonblinking emission intensity. We demonstrate that lifetime variations are due to switching between the neutral and negatively charged state of the nanocrystal. Negative charging results in faster radiative decay but does not appreciably change the overall emission intensity because of suppressed nonradiative Auger recombination for negative trions. The Auger process involving excitation of a hole (positive trion pathway) remains efficient and is responsible for charging with excess electrons, which occurs via Auger-assisted ionization of biexcitons accompanied by ejection of holes.