June,
It sounds like this baby might be very flow dependant. Sometimes low 
energy babies are. Have you tried using the syringe to deliver milk 
while you do the suck exam? It makes a very big difference. All that a 
baby does on a finger is non-nutritive sucking. At first they may try 
extra hard by using more pressure to see if they can get milk from the 
finger. Then a baby who is tired or has low energy reserves due to a 
cardiac, respiratory, neurologic disorder or just due to not getting as 
much milk as he would like and being in "energy conservation mode", he 
is more likely to not bother sucking well unless he is getting a good 
flow for his effort.
This is the time that using a supply line or Lact-aid is ideal. It keeps 
the flow strong, so the baby finds it worth his while to work at the breast.
Too bad mom is so overwhelmed. Perhaps encouraging her to keep pumping 
for a few days and feed this baby in the easiest way will allow her to 
remarshall her own energy, and perhaps be willing to try something else.
Catherine Watson Genna, IBCLC  NYC

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