A long-standing discrepancy exists in determinations from observations and modeling of the diurnal variation of the peak electron density of Saturn's ionosphere. Using a new Saturn-Thermosphere-Ionosphere-Model (STIM), we examine the suggestion by Burns et al. (1983) that Saturn's rings shadow its ionosphere causing radio penetration holes, thereby allowing lightning-induced radio signals (Saturn electrostatic discharges, SEDs) to escape. This lessens the need to invoke globally enhanced loss processes to account for Voyager era observations of nighttime peak density (Nmax) as low as 103 e/cm3 from the SEDs. We find radio frequency windows produced by ring shadowing that were narrow and confined to low latitudes during the Voyager era, but are now broadly distributed over northern mid-latitudes during the Cassini era. If lightning sources occur only at near-equatorial latitudes, then the far less frequent detection of SEDs by Cassini early in its mission would be consistent with the current ionospheric morphology.