Pappa,
I don't know how a modchip like this would react to such a thing, but do you have to reset your clock in the Sony browser when this happens? If so the 2032 battery may be weak. That may explain why it works until you unplug it.
Myself and several other posters have found that if the CC is not warm, fuzzy, and happy it will boot from it's on board backup firmware, so I wouldn't be surprised if a weak backup battery would cause this behavior.

