Every sentence must have at least one main clause. A main clause contains an independent subject and a verbal structure and expresses a complete thought. A fragment occurs when you neglect to insert a main clause somewhere between the capital letter at the beginning and the end mark concluding the word group.
The sentence containing the fragment is:
B. Our dog loves to retrieve sticks. He will beg you to throw them for hours. Even if it's clear that he is exhausted.
The exact Fragment is: Even if it's clear that he is exhausted.