IPhone takes long time to wake up when I have a notification?

I have an unlocked AT&T iPhone 4 and whenever I get a call, text, email, or any other notification it takes a long time for the phone to wake up from stand by. This only happens when I get a notification, not any other time. It's jailbroken on iOS 6.0 but I had this problem before I jailbroke it. It has no warranty so I can't send it back to Apple. Any other suggestions?

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