When mine started doing this, it was due to a short in the dock connector. Likely the same short that started causing the brief messages (which eventually became longer, repetitive and persistent) saying "This accessory is not made to work with iPhone...etc"
Try hooking it up to a computer to see if it still does it.
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8 gig iPhone, no service (jailbroken on 2.1 to activate it as a suped up iPod touch) - 33 applications installed, updated to 2.2
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