quod agat is a relative clause of purpose.  In a relative clause of characteristic, a relative pronoun is followed by a verb in the subjunctive, which tells what the relative pronoun typically does.  Generally, this is translated, "which is of the sort that verb."  nil quod agat translates "nothing which  is of the sort that it does."  quod modifies nil. Martial is implying that the third cough will not cause Aelia to lose anymore teeth since she has already lost them all.