Explanation:

Correct Answer is (d).The part given in bold in the sentence is not correct since there is the error of usage of double negatives in this part. This is not grammatically correct to use double negatives and that is why, it needs to be replaced. Now, coming to the error, there is double negative and one should be done away with to make the sentence correct. Therefore, has failed to produce any valid reason should be used here.
The correct sentence is:
He has failed to produce any valid reason to keep him in the job despite his irregularity and insincerity towards the work.This makes option D the correct choice among the given options.