I have a 2005 corolla S 2.2 and the battery will die if not cranked every day.

You need to test for parasitic current.

New may not be the solution as the batter may be partially bad (self discharge) or the alternator may be leaking current back flow through the diodes.

Need to measure the current drawn to see what you are actually dealing with. The usual method would be to use a VOM and measure in series with the battery. IE: unhook the positive and connect the VOM from the battery + to the + cable, with the meter set for current. I suspect it's normal to draw some current when not running. IE: clock, random EVAP purges, etc, etc.. But it should not run down in one day. I have a 2005 CE, and I've sometimes gone a few days without starting. I only recently ran the battery down in that car for the first time, but it was from me sitting out in the car and using my laptop to get on the interweb when the house desktop was busy... I underestimated how much current the laptop would pull, and ran it down low enough to not turn the starter over.. :( I hate doing that.. It's not good for a battery to discharge it. But I slapped a charger on it pronto and got it back up to normal.

Anyway, until you actually measure and know what it's pulling, there is little one can do. If it's pulling more than normal, you could then start backtracking the circuits and pull fuses for each until the current draw drops out.

The thing is... I'm not really sure what is normal.. I've never checked it on mine. It could be the battery or the new alternator, but the auto parts store can probably check those. A bad diode could cause that, and not charge properly when running. But it could be a lot of other things.. IE: make sure the trunk light is not on, etc..

A manufacturing problem with the battery can make a new battery act like this.