Was the Fountain of Magical Brethren remade after the fight between Voldemort and Dumbledore at the end of Order of the Phoenix, before it was changed for the Magic is Might statue of wizards sitting on Muggles during Deathly Hallows?
We don't know.
We don't see anything of the Ministry of Magic in book 6, which is the time-period you're asking about. My best guess is that it was probably removed since Dumbledore says that it was "destroyed" during the fight in the Atrium.
"The fountain we destroyed tonight told a lie. We wizards have mistreated and abused our fellows for too long, and we are now reaping our reward.”
(Order of the Phoenix, Chapter 37, The Lost Prophecy).
Why he says destroyed I don't know. Two of the statues were hit by Avada Kedavra. But I would have thought that it'd be nothing a bit of Reparo couldn't fix. Nevertheless, maybe the fountain was beyond magical repair for some reason. Or perhaps the Ministry decided to replace it with something more appropriate seeming as it was now the headquarters of the fight against the Death Eaters. All we know is that by Deathly Hallows the fountain is gone.
Previously a golden fountain had filled the center of the hall, casting shimmering spots of light over the polished wooden floor and walls. Now a gigantic statue of black stone dominated the scene.
(Deathly Hallows, Chapter 12, Magic is Might).
What happened to it remains a mystery.