Transformation of sentence

"In succession" looks wrong - did you mean "consecutively"?

Mary did not give up despite failing in successive attempts OR Mary did not give up despite having failed in successive attempts.
Or consecutive could be used instead of successive, but in any case I believe you need attempts or efforts.

Mary did not give up despite failing/despite having failed his exams in succession.

Would it be correct if I add 'his exams' in the sentence?

Thanks.

Here you introduce two new aspects to the phrase EXAMS and HIS.
You have failed in your earlier examples to show that what was failed is exams and that the setter of those exams,was in fact a male.

Mary had studied for his urine test but, in the transgender oral exam, found no succour in a succession of unsuccessful attempts before finally succumbing.

My apologies. The pronoun be 'her', not 'his'. Should have been more careful.

Mary did not give up despite failing/despite having failed her exams in succession.

Would it be correct if I add 'his exams' in the sentence?

Thanks.

I think replies which are nonsensical should be deleted.

Okay,because of the changes you have made in introducing EXAMS and HIS/HER lets go back to basics.
I would eliminate any use of (succession/successive/consecutive) and (his/her),and replace with 'previous attempts" and 'the'.

Then the sentence would be expressed like this:
Mary did not give up(despite failing/despite having failed) the exams at a number of previous attempts.