As well as all the wonderful suggestions already presented, I
usually do some active listening to find out more about the mothers
situation.  Sometimes the whole situation can be solved in another way than
leaving an unwilling baby.  If the mother is a first time mother (and
usually they are or they wouldn't be phoning for this kind of help), and
sometimes with multips, I also talk about parenting and the difficult
decisions we have to make and that everyone wants what is best for baby but
don't always think about the goals that we are trying to achieve.  For
example,  we may want our children to feel secure and loved but don't think
about the effect on that goal when we decide to leave them because we need
to get out.  I try to point out the choices that the mother faces in her
situation, their effects on the child and ask the mother to think about what
her goals are.  Then I talk about parenting as a long term activity and how
this is the beginning of a lot of tough decisions that don't become any
easier, only different.  All of this, of course, has to be done with
diplomacy and lots of active listening, but I believe it is an important
part of being able to help mothers not only to continue to breastfeed but
also to think about what they are doing in order to grow into loving
parents.  Maybe its my LLL background coming out but I do think it is an
important part of breastfeeding counseling to empower and educate women to
make decisions.
Jennifer