The correct answer is: D. No error
The sentence is grammatically correct. The conjunction “but” is used to join two independent clauses, and the adverbial clause “though very weak” is used to modify the verb “is.”
The sentence could be rewritten as follows:
His father died of cholera, but his mother, though very weak, is out of danger.
The sentence could also be rewritten as follows:
His father died of cholera, but his mother is out of danger, though she is very weak.