How old is your battery? Batteries can go out as soon as two years after you buy them depending on your driving habits and what kind of battery you buy. That would be the first thing I suspect if it's more than two years old. Check the terminals for corrosion and while you're at it make sure the connections are tight- a loose ground or loose positive will cause problems. If you have access to a multimeter read the voltage across the terminals, if it's below 12 volts there is a problem; the battery is not holding charge or it isn't getting a charge from the alternator. Turn the car on and read the voltage again, if it reads above 13.5 volts your alternator is probably still fine and it's probably the battery. That this problem crops up mostly after the car hasn't been run for a few days further supports the bad battery theory. A bad battery or loose connection can cause random problems at lights when the alternator isn't putting out much juice- especially if your idle drops too low. My sister's car would lose stereo power, the lights would dim, and the AC would cut out all randomly at lights- it turned out the simple fix was tightening a loose wing nut on the positive battery terminal.