my speakers did the same thing, front left stopped working then the front right started going on and off at almost random. After reading around its common with the stock speakers that they just over time shit out. If you aren't into amazing speakers id say go grab a pair of pioneers for $40 from best buy or auto-zone they are far better then stock and will probably fix your issues.
these are OEM speakers? well if so then i would say upgrade them because they are pretty cheap to begin with and there is a decent amount of water that gets between the door and the inside door panel where the speaker wire goes so in the morning the moisture might prevent them from working
Yeah replace the stockers. They're made so thin I can snap one in half. lol
2010 Cobalt 2LT Victory red Coupe
Mods: Tinted 50% ceramic all around, factory spoiler, 2008 LE5 2.4 Throttle body, GMPP Intake, Walker stock exhaust system (back to silence), TruBendz/MBE 2.5" catted Downpipe, HP Tuners by Chenry Motorsports, Alpine CDE-151 with USB port, Rockford Fosgate 300-10