We present measurements of the electron phase coherence time tau(varphi) on a wide range of open ballistic quantum dots (QDs) made from InGaAs heterostructures. The observed saturation of tau(varphi) below temperatures 0.5 K<T(onset)<5 K is found to be intrinsic and related to both the size and the openings of the QDs. Combining our results with previous reports on tau(varphi) in GaAs QDs, we provide new insight into the long-standing problem of the saturation of tau(varphi) in these systems: the dwell time becomes the limiting factor for electron interference effects in QDs at low temperature.