If a student experiences extreme anxiety, how can I be supportive without lowering academic expectations?

It is best to set up a private meeting with the student and state that you have noticed she becomes very anxious in response to stressful academic situations. Ask the student what support measures she would find helpful in reaching his optimal performance. Do not ask her if (or suggest that) she has a disability, but encourage her to make use of a list of campus resources (that may include the disabled student services office) that she might find appropriate.