The dock port on your iPhone may be damaged, or the usb port on your computer may be damaged or broken. Check to make sure that your cable is plugged in securely on both ends, and there is no obvious physical damage. Other reasons could be the usb software of your computer could be set up wrong. Also check that your iPhone and version of iTunes are compatible, or you may have to upgrade to the latest version of iTunes. If none of that works, contact Apple support.
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Your iPhone may not be connecting to iTunes if there is an update needed. You can restart your phone after updating and see if that solves the problem. If not, contact Apple support.