Anxiety Support Group
Anxiety is a physical condition marked by intense and persistent feelings of distress, fear, angst or dread. General anxiety caused by routine day-to-day stresses usually passes quickly and is experienced by almost everyone at one time or another. However, such feelings that linger over time and are very difficult to cope with, and which lack a clear cause, may indicate...

Tell her to go on stage or just lip synch.
Tell everyone else to completely ignore her when she fails to get on stage. Make it an emotional non-event with no beneficial psychological outcome to her of attention or petting or poor you-ing. Leave it alone to be its own thing.
She's probably getting massively positively reinforced every time she fails, or does the mea culpa about failing. She has to swallow her own mea culpa. That's a consequence of her actions, not her anxiety. How she feels about what she does or does not do is a piece of the decision to act that belongs to it, and which she needs to carry on her own.