Ranking adjectives (e.g. first, last, second, third, next…) can and often do lose their ranking power.
Think of “a third visit” as one after two previous visits without lining them up in an orderly (temporal?) sequence.
For example, let’s say your previous two visits were unpleasant experiences.
Will there be a fourth after the unsuccessful three?
I think you needed a second opinion. And how about “next June” versus “the next June”? No doubts here?