Sounds like the baby may have a disorganized (or dysfunctional) suck...perhaps caused by the frenulum to begin with, or in addition to the frenulum issue.  If the baby has low muscle tone in his mouth, feedings will be poor.  How are his cheeks?  Can he maintain tongue cupping?  Phasic bite rhythmic?  There are lots of little clues to determine what the shortfall is.  This baby might benefit from a visit with a Speech Language Pathologist (SLP) or Occupational Therapist (OT) to look at strength and coordination.  It's important to find an SLP or OT that works with pediatric feeding ("Do you offer services for pediatric feeding?")  If you can go *with* the mom for the visit/s, you can ask questions and learn what they are looking for, and what types of exercises they do, and continue to help the mom as baby becomes stronger and more coordinated.  I have found that after 6 weeks of age, it takes substantially longer to overcome these problems, so the sooner she meets with someone the better.  
Looking forward to hearing the resolution.
Amy Peterson, BS, IBCLC

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