We measure the effect of dissipation on the minimum zero-bias conductance, G(min)0, of a superconducting single electron transistor (sSET) capacitively coupled to a two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Depleting the 2DEG with a back gate voltage decreases the dissipation experienced by the sSET in situ. We find that G(min)0 increases as the dissipation is increased or the temperature is reduced; the functional forms of these dependences are compared with the model of Wilhelm et al. in which the leads coupled to the sSET are represented by lossy transmission lines.