Why won't my iPhone 4 auto connect or auto recognize previously used Wi-Fi?

I just got an iPhone 4 (which I'm loving!), but every time I turn the phone off (lock it down), it seems to disconnect from my home's Wi-Fi. Then, when I open/unlock the phone I have to re-connect to my house's Wi-Fi.

Is this normal? I can't imagine that this is supposed to be the way it is, because my iPod Touch instantly recognizes my home Wi-Fi and other previously used Wi-Fi locations and automatically connects to them when in range. How can I get my iPhone to auto-connect to previously used Wi-Fi?

Added (1). I have "Ask to Join" turned off.

Do you have the Ask To Join Network on?

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