Lisa,
Interesting that this baby does better when drowsy.  Is he the type who gets
all frantic when he's awake and not immediately attended to?  Babies who are
having trouble organizing a bolus of milk for swallowing (as when mom has an
overactive MER) often nurse better when drowsy.  Is he a gulper?  This is a
very interesting problem.
Catherine Watson Genna, IBCLC