the external quartz (10Mhz) starts every time (although with one particular µC, it was taking 10s to start, sometimes... ).
you definitely have a problem here. a) are the traces to the xtal less than 1cm? b) are the traces to the 2 small caps less than 1cm? c) do you have 10-100nF and 4.7-22 uF acriss the LPC with extremely short traces?

PS : BTW, any idea what that statement (LPC922 datasheet) exactly means:
During a power-up sequence, the RPE selection is overridden and this pin will always function as a reset input. An external circuit connected to this pin should not hold this pin LOW during a power-on sequence as this will keep the device in reset.
Does that prohibit the use of external supervisor?
not at all, what they (try to) say is that if you, when using this pin as a regular input, for instance connect it to 'Q" of a flip Flop that is reset at power up you will never get out of reset.

maybe a better phrase would be "not hold this pin LOW after a power-on sequence"

Erik