Sentence I talks about a doctor, who did not catch a ball and sentence II talks about the character of the doctor. It can be noted that sentence II is a condition that is in favour of the doctor but still, he/she could not catch the ball. So, the connector/s must indicate the relation between the two sentences.
Accordingly, 'despite' (in spite of) is the only connector that matches the context of the given sentences and can thus be used.
Although- however; but
But- used to introduce a phrase or clause contrasting with what has already been mentioned
Nor- used to introduce a further negative statement
Hence, the correct answer is option (d).