Good Question.
I got B.
I thought its between B and E.
(A) on playing, even though he had injuries that recurred over and over again, always hoping to return back - too wordy. the modifier phrase after comma is far too lengthy
(B) playing, in spite of recurrent injuries, always hoping to return - best . Short and concise
© playing, though injured over and over, and he was always hoping to return back - supressing the phrase we get ...continued playing and he was always hoping ..sounds awkward- Non-parallel structure.
(D) on playing, even with injuries that recurred, and always hoped to return - - playing and he always hoped ..Non parallel
(E) to play, despite recurring injuries, hoping that the return - looks ok at first continued to play, hoping ... But that the return to his Makes it awkward