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Originally Posted by bob jenkins
I agree. I don't see (either way) a clear answer in the book.
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Rule 7 Section 2b & notes give us a pretty good hint.
b. It is not mandatory that a player be designated to bat for the pitcher. If
the pitcher is listed in the starting batting order, the pitcher automatically
becomes the DH. In this case, the pitcher is to be considered as two
players, both pitcher and DH, and can be substituted for as such.
Note: For substitution purposes, the pitcher is not to be considered a defensive
position.
So as two separate players, when I have the P/DH replaced on the mound I would assume he is still the DH until otherwise notified. Should a new batter come to the plate in the DH position after that I'm going to stop and confirm that this is a simple DH substitution.