Yes the Down Syndrome definately presents certain challanges. A baby with
Down Syndrome is probably hypotonic (low muscle tone) and may, or may not,
have decreased alert states, either in duration or in quality. The down
syndrome babies I have worked with have run the spectrum of nursing skills,
from excellent to poor, depending on many factors. The normal heart is a good
sign. At this point check for dehydration. If this baby is not dehydrated,
which would increase sleepyness, I would suggest that you first consider the
position (s)he is being nursed in. Low trunk tone requires increased trunk
support- have you tried using either the cross cradle hold or the football
hold? Both these positions offer increased trunk support. Also, try to
support the baby's extremities as much as possible; get the baby into as much
flexion posture as you can. This is a little tricky- because this is also the
position that encourages sleep! Does the baby also have low oral tone? This
will decrease suck strength, the volume of milk the baby gets, and subsequent
supply.  If you don't feel qualified to assess oral tone, find an OT or
Speech Therapist who can. There are oral motor exercises that can increase
oral tone. If low oral tone is present, the use of chin support may help, as
well as facilitate a swallow. Ask an OT/ST how to do this. This child will
probably be seen by a variety of therapists in the coming months/ years, so
try to find a breastfeeding friendly one now.
      This is a challanging situation.  I personally have found the Haberman
bottle to be an effective tool to use to transition to the breast, because
with it used properly you can vary the flow, depending on the baby's state of
alertness. My first preference would be a supplimentor, which would keep the
baby at the breast and increase the volume of milk the baby receives before
the baby falls asleep. If  mom has an overactive let down, I would still use
the supplimentor and pinch it off when mom feels a let down, then open it up
when not, as  baby may not be sucking hard enough to get the volume needed
during the low flow valleys of a normal nursing session, which is when the
baby may be falling asleep.
      Good Luck, and keep persisting.

Debbie Rabin, OTR, CLC
Los Angeles, CA