This is the type of situation where a nipple shield is a very useful tool. I'm assuming the mother has been expressing her milk to establish her supply, as well as provide milk for her baby. Test weights using the shield will confirm whether the baby is transferring an adequate amount of milk, which is entirely possible. If test weights are not possible at this time, it may be prudent to continue to express milk in addition to nursing with the shield until adequate intake/gain can be assessed. 
For the mother and for the non-latching  baby, the experience of  nursing with a shield is much more satisfying than other feeding methods and the closest thing to nursing at the bare breast. It also creates a more "breast friendly" feeding experience that syringe, cup or spoon feeding can't provide.  In my experience as a lactation consultant, babies almost always will give up the shield, some sooner than later. Sometimes "tincture of time" is needed to allow babies to latch well. Given a choice of spoon feeding for two weeks or using a nipple shield for two weeks - that's an easy choice for most mothers. And easy doesn't  mean wrong. It means it is sustainable and practical, and less likely to end up with breast milk in a bottle.

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