I know 3 different people who interviewed at a program (high-level programs), were waitlisted, didn't get in, re-applied 1-2 years later and are now students at the place they had initially been rejected from.
People have different experiences with re-applying, and I think it entirely depends on why you were not offered admission to that university. If someone interviews and the PI realizes maybe the school isn't a good program for the student's career goals, or the PI realizes the student isn't a great research match/fit, or maybe even that the student's personality didn't mesh with their own or the culture of their lab, etc - applying a second time probably will not improve your chances, and you probably will not receive an interview. But if, for example, there were a few students that the PI wanted to take and someone just barely squeaked out ahead of you, and it was a tough decision -- I imagine they would be thrilled to have another opportunity to interview you and offer you admission (especially if additional experience has been gained).
I also work at a university in research (I'm going to be a 1st phd student near year at a diff school), and have talked to faculty where I work who have said re-applying just shows how interested you are, and reiterated that it really depends on why the student wasn't accepted (it is was lack of fit, or having someone slightly more competitive take the spot even though they really liked the candidate). And that's really what influences whether you get invited back.
If it's a school you genuinely enjoyed interviewing at and it was a PI you truly want to work with, and it's a program you would like to attend, why not re-apply? Sorry this turned into a novel - I just don't see the harm in re-applying if you really liked the school and it's a top choice (unless it would cause financial strain, etc., which is totally understandable)!