Syringe feeding for that long is worrisome.  If the timing isn't just right, it can disorganize the swallowing pattern. 
I'm glad the baby breastfed in your presence, but the "40 minutes" worries me.  Check how often the baby swallows.  I look for 20 or more swallows in a row before baby pauses.  If she is swallowing less than 8 times in a row, she is burning more calories than she is consuming.  I would try supplementing at the breast with a tube to speed up the feeding.  Or, if baby tires as the feed progresses (as she probably will) and compression isn't enough, I'd suggest supplementing at the end of the feed with mom's milk in a slow-flow bottle that gently flares at the base.  Once baby has the stamina to swallow more frequently, breastfeedings usually improve, too.
Amy Peterson, IBCLC
Idaho

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