Which is correct:
I felt strong for the last three miles of the race.
or
I felt strong during the last three miles of the race.
Which is correct:
I felt strong for the last three miles of the race.
or
I felt strong during the last three miles of the race.
The former is correct.
Both sentences are grammatically correct.
The latter is also correct.
The meaning of either can be the same, that while running the last three miles of a race you felt strong. However, the former could be stated to mean that leading up to the final three miles of the race, you felt like you were going to be strong for them. Then a qualifier would probably be needed to differentiate the two.
"Ten miles into my half marathon I felt strong for the last three miles of the race; however, during those three miles I really broke down."