One change I'd make in Brixton's talking points is that I would NOT say that "I find myself being angrier than I should be." That shifts the emphasis to your emotional response, and to its appropriateness. Try to be a neutral judge of her actions. (I'm not saying don't BE angry; I'm saying don't make your emotions the issue when you discuss this with the student.)
On preview, Ex_Mo, perhaps then you could also talk to her about the perils of taking on too much and the need to put her own health first. Clearly this student (well, like all of them) deserves compassion.
+1
You might want to frame any discussion you have with her with respect to the client. This is not just about her actions and how they affect her performance. She's working with a group and if something really did come up that affected her ability to finish her part of the project, then she needs to be honest about it with her "coworkers". She has a bridge to mend with you if she wants that letter, too.
Alan
Yes, as this class is constructed to be a "real world" experience, framing the discussion as the problem affects the client is good -- but also as it affects the group.
And this can be a reason to consider (just consider) acting opposite to the advice here to handle this privately.
I've taught a similar class, and I've dealt with similar problems, and I've resorted to handling this as an exercise for the class as more "real world" experience toward management.
First, of course, do verify that the LMS record is reliable. If not, then. . . .
I handled this sort of thing openly in that class but naming no names. "One of our classmates has [in that case] caused a serious problem for the client which affects all of you -- although only one of you knows which of you is the one who did this. Let's leave it that way and discuss this as if it were one of our case studies. Now, how do we first identify the problem -- not the person, the problem -- and then, let's discuss options for solutions. . . ."
In this case, the client was ready to withdraw, by the way.
Anyway, this ended up being an extraordinarily good discussion and with a good resolution. Just a thought.