When I plug in my keyboard's bluetooth dongle to the USB port, my Raspberry Pi boots up. When I take it out, the power seems to instantly cut (screen goes black, Pi unreachable by ping/ssh). Note that this is the opposite of the normal not-enough-power situation - again, having the USB device plugged in seems to enable the power, rather than draw too much. This does not happen every time (last time the Pi did not have the device attached it was up for ~250 days) but is very frequent.
What could be causing this?