This paper reports on an investigation of dynamic behavior of an electrostatic Vibration Energy Harvester (e-VEH) which uses gap-closing capacitive transducers and operates in a constant-charge mode. This work provides a deep insight into stability issues of a e-VEH investigating four dynamic modes, among which only one corresponds to a regular, stable and desirable operation mode needed for the energy conversion. The three other modes represent instable behavior. Each one corresponds to a particular range of external acceleration, and in none of these modes the e-VEH behaves similarly to an ideal constant-voltage biased transducer associated with a resonator. This paper describes a modeling experiment allowing a demonstration of the four operation modes, and proposes theoretical considerations for their quantitative description.