My girlfriend gets this, and I have spent ages trying to find out what it is. Whenever she gets extremely upset or depressed about something, she usually vomits - but never when I'm around (she says she doesn't want to vomit in front of me, despite me telling her that it is perfectly okay, and because of this she forces it back down - which I tell her isn't good for her).
She does have a problem with food, and recently has been feeling sick after every meal that she eats (the vomiting due to depression has been there ever since I met her - 2 years ago). She doesn't eat an awful lot, and consistently worries about her weight when she is not overweight at all (if anything, nearly in the underweight category of the BMI scale).
I've read out about 'psychogenic vomiting', which seems one of the closest medical explanations I have been able to find, and - because the distress is mostly caused by a loss or separation of a loved one, mild 'separation anxiety disorder' could be a factor in it.
Hope this will help other people and hopefully eventually help towards defining and lessening the depression/anxiety-linked vomiting in my girlfriend's case.