One of the few things I see often leveled as a criticism at Utena is how repetitive some things can be. Mainly the entrance to the Battle Arena.
For me it wasn't a problem, the music was so awesome I loved it every time it came on. Even though I binge watched the whole thing in one day.
The sequence is often compared to a Magical Girl transformation scene. And it does have aspects of that, which are played up even more in the movie when the same song is played as Utena is transformed into a car.
But it's also like a ceremonial ritual. It has to play before each battle, just as in Pro-Wrestling each wrestler has to come out to the ring with their theme song playing.
More ritualistic then that even, especially when you get to the 3rd incarnation of it.. And the lyrics of the song do have pretty significant meaning once you understand all the layered themes and symbolism of the show.
So basically, no, it's not something I ever get sick of.