Personal identity, in my view, rests entirely on mental traits
(memories, personality, habits, knowledge, etc.).  The particular
hardware which supports and implements these traits is
irrelevant.  Under this assumption, gradual replacement is no
different from discontinuous replacement. Let the surgeon replace my
neurons one at a time, or all at once.  Even let my brain be
taken apart completely, wait a week, and then reconstruct it with
different hardware.  In any case, the resulting brain is
functionally equivalent to the one before the operation -- and
this is all that matters.  The patient survives, the same person
before and after.
<P>
(Note, too, that if the surgeon is imperfect, and fails to
replicate the original brain completely, we are not befuddled --
we merely say that the patient <I>mostly</I> survives, and is <I>
mostly</I> the same person afterwards. We would describe most
current-day brain surgery in the same terms, for that matter.)