I have seen guidance go both ways on this one, and I suppose that I should preface my remarks with the warning that I am not a lawyer or dispensing legal advice... check with your own counsel for authoritative interpretation of this situation and use at your own risk.
At first glance the law, 26 UC S132 would seem vague on what they mean by "first four years". There is Publication 970 which is intended to be correct and informative, but not authoritative on this matter which seems to be explaining (pg 11) that fourth year is considered being a "senior" in an undergraduate program, presumably no matter how many years it has taken to attain that standing. The key, of course, is that you don't take the AOC credit more than 4 times altogether and is not a graduate student.
A document from the IRS, "Education Credits: Questions and Answers", Q17, also non-authoritative, but explains that "[the taxpayer is] not required to claim the credit for a particular year. If your child's college does not consider your child to have completed the first four years of college at the beginning of [2020], you may take credit in 2020." Thus it seems the IRS recognizes where the four years of eligibility are not necessarily used up by time in school, but instead by how many times the credit is claimed.
I am not aware of PLR's or rulings or cases which further define this situation, but it seems a very reasonable position to hold.
