How can I make the App Store remember my password?

Solution 1:

Download "password pilot" in Cydia (the jailbreak app store) it will save your password so you wont have to keep entering it.

Solution 2:

You can't change this behavior. Although, when you download a free app, you have to enter your password; if you download another free app immediately after, you won't have to re-enter your pass. That's as close as you're going to get to a remember password feature on iOS 5.

This is something that was intentionally in place and now it's intentionally changed on iOS 6 to reduce the need to re-enter your password just for updates.