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This is the context:

One is a published case of a patient who was locked-in classically with a brain stem injury and had an unusual extension of the injury into the auditory system. The auditory system is usually very well preserved because it goes to both sides of the brain. But this person ended up with a central auditory agnosia, which means the patient could hear but couldn’t really put together complex sounds; the condition was not recognized for many months because the patient relied to an extent on lip reading. However, during tests of the patient’s cognitive level, the lip-reading would fail and it seemed like the patient inexplicably fell off the curve and was, consequently, judged to be minimally conscious or cognitively impaired. It wasn’t until a colleague of mine finally decided to draw and write questions for the patient that it became clear that he was fully conscious and just needed to have the visual representation of the words. So in this case, the patient was locked-in and conscious.

source: The enigma of human consciousness.New York Academy of Sciences.

What is the meaning of "fell off the curve"? I googled and find nothing about this phrase. Can anyone explain this?

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The curve refers to a standardized graph probably of responses to questions that quantify how aware a patient is. As @Jdrupal mentioned in an answer, there's a growth curve that shows percentiles of weight or height versus age for children. If a child "falls off the curve" that could mean that they are very thin for their age.

The patient this quoted case wouldn't be able to respond properly if asked verbal questions without being able to lip read, so didn't appear to fall "on the curve" and be cognitively aware.

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