Paula,
I'm behind in reading posts, so forgive me if this (from July 6) has been
addressed by others.
First---empathy!  Mine with you.  I've had days and babies like that.
Second---sounds as if the baby was REALLY aversive to the breast.  It has
taken me years to realize that we need to listen to babies like that.  If
they are arching, pushing off, crying, or else shutting down and ignoring
what we do, then nothing from my bag of tricks is going to help.  Not then,
anyway.  Persisting just makes the mom and LC more frustrated, and doesn't
improve the mom's trust in the LC.
So, in cases like this, I think it's best to encourage the mom
1) to pump and maintain a good supply;
2) to feed the baby with whatever method works for her and the baby---even if
it's a bottle [gag!]---but at least a bottle with a teat that reaches well
into the mouth, not a playtex nurser;
and 3) take care of herself so she can continue to work on teaching the baby
the breastfeed at a pace the baby is comfortable with.
I learned a lot from Nicholas and his mother.  He took 12 weeks to learn how
to latch on, despite being the healthy full-term baby of an experienced
breastfeeding mom---she had nursed three kids up to 3-4 years each.  I
visited once a week; we'd try him at the breast; he'd fuss and arch and
resist; we'd back off and I'd give her a pep talk about how great a job she
was doing against all odds.  She treated him like a nursing baby---carried
him a lot, slept with him, fed on demand.  She hated the pump---could only
keep one bottle ahead of him.  He was a fussy, tense and grouchy kid.
The day he finally latched on he lay next to her on her bed, nursed until he
fell off asleep, and was as soft and smooth as butter.  In the next two days
he learned to latch on reliably and fed for close to a year.
The key is for us to let the mother and the baby tell us what they are
comfortable with.
Peace.  Chris