stereo draining battery??

Um, who installed it? Something is not right with the installation at all. Sounds like the power source is coming from a constant 12v source (like constant even when the car is off). Check the installation if you did it yourself, or if you had a place install it for you, take it back and have them redo it. No a capacitor will not help, neither will a new battery. Dont add more components onto your car to fix what could be, and probably is, a very simple wiring problem.

you may want to check your wiring harnessand check that the colors match, normally yellow is memory and this get power at all times so it can save your presets and time, and every deck will allow you to eject a cd with the car off it's just for convinience. and the red wire is the one you want to check that is the ignition wire this should be connected to somethig that's only hot when the key is turned to the ON position. if you have a volt meter just measure the voltage from the yellow and red wires on your harness behind the deck and let me know what you come up with.

Yep it is wired wrong. As stated your red wire which is your turn on wire should not be getting power when the car is off.