Why do I have to keep inputting my email password on my macbook air? A few times each day, the email logo bounces up and down and asks me to (again) input my aol password. Why is this? And what can I do to stop this happening?
I'm not understanding why this is happening with you. Well basically, you can say your mac is "forgetting" your Apple ID / email or whatever. If this situation is related to an Apple ID, using The Mac App Store, logout and login and tick the "Don't Forget"

You can use Keychain Access! You can modify which applications will automatically log you into your email while starting the application.