Orbital observations of the surface of Mars indicate that ancient basins were once host to lakes that may have been depocenters of sedimentary materials, including hydrated minerals like phyllosilicates. Later volcanic and sedimentary resurfacing may have developed a stratigraphy within the basins detectable through radar sounding data from the Shallow Radar instrument. Our radar survey of 61 open basin lakes (OBLs) revealed only one plausible reflector in a single basin east of Hellas Planitia. We investigated possible factors contributing to lack of radar detections in the other basins through detailed analysis of radargrams and subsurface characteristics of OBLs. As possible hosts to previous habitable environments, OBLs on Mars are important sites for future robotic and human missions. A full understanding of the factors influencing the radar signal, as addressed here, is important for more fully characterizing the subsurface structure and geology at these locations.