Sounds like something else besides the stereo is draining the battery dramatically. Just like what Iceman says, how old is the battery? When you have just ACC switch on, the alternator cannot charge the battery just to let you know.
If you have access to a fluke or Digital Multimeter, run positive lead to positive side of battery terminal and negative to negative. Hold it there for about 10 seconds and while holding your leads onto the posts, remove the negative terminal clip (10mm or 12mm) with the dmm lead still on there, you should still maintain 12.45v or higher, if it starts dropping after negative post is removed, then you have a parastitic drain.
2009 Cobalt LS XFE U74
Mods: K&N Typhoon Intake, Option Cat-Back Exhaust, Cosmo Short shifter, Maxxim Ahead 17X7's, MPx shorty antenna, FE5 Strut/shocks, Tein S Techs, Moog endlinks, Moog spring seaters, ZZP shorty header, LSJ downpipe, LNF front grille