What makes you think you deserve a second chance?
"A second chance" means "another chance", although it couldn't be his "seventh" because the implication is that he has had only one so far. "Second" does still mean the one following the first.
But, yes, it is another in an undetermined number of chances, although in drama the second chance is so often the last. You might hear a character say something like:
"We've given you a second chance, do you think we can just keep doing it, giving you another, and another. We've got to draw the line somewhere".
not a teacher
Student or Learner