Green’s Dictionary of Slang

cork n.2

[one’s mouth is stopped with a cork]

(US campus) the absolute inability to answer a question in class or to recite a passage from memory.

[US]B.H. Hall College Words (rev. edn) 133: cork, caulk. In some of the Southern colleges, this word [...] signifies a complete stopper. Used in the sense of an entire failure in reciting; an utter innability to answer an instructor’s interrogatories.
[US]Monroe & Northup ‘College Words and Phrases’ in DN II:iii 138: cork, n. Failure in recitation.