[_Q_]

It seems like occasional rejection or disappointment is a fact of life, though, and not being invited back is just one example of that. This doesn't mean that it doesn't hurt, just that everyone experiences it at some point in her life. A PNM who is dropped by all the houses might feel very alone. I might consider sharing a story about a time when I felt hurt and rejected, but ultimately survived. Maybe it would help to point out that the recruitment process can be sort of arbitrary. It doesn't mean that she's a worthless person, just that she might not have happened to meet women she clicked with, and the house may have been forced to release a certain number.
Although Greek life is very important to some people, the PNM probably has other interests and goals too. Maybe it would be possible to talk with her about what she genuinely enjoys, and help her find student orgs that match her interests. If rushing again is a realistic option for her, being involved would probably help her chances.