Why is Harry's & Voldemort's prophecy not repaired with something like the "Reparo" spell? Why is it lost for good (and Voldemort angry at Malfoy for that)?
It wouldn’t help - the prophecy escaped when the ball broke.
It might have been possible to mend the glass sphere that encased the prophecy, but the reason the Dark Lord wanted it was for the prophecy inside the sphere, which escaped when it shattered.
“He gave another stupendous heave and Neville’s robes tore all along the left seam – the small spun-glass ball dropped from his pocket and, before either of them could catch it, one of Neville’s floundering feet kicked it: it flew some ten feet to their right and smashed on the step beneath them. As both of them stared at the place where it had broken, appalled at what had happened, a pearly-white figure with hugely magnified eyes rose into the air, unnoticed by any but them. Harry could see its mouth moving, but in all the crashes and screams and yells surrounding them, not one word of the prophecy could he hear. The figure stopped speaking and dissolved into nothingness.”
- Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)
The record of the prophecy had disappeared, so fixing the ball that contained it wouldn’t help - it’d just mend the sphere itself, not put the prophecy back into it. Reparo seems to only be able to put together pieces that are still present in some way - it can put liquids that spilled on the floor back in their jars, but the liquids haven’t disappeared. They’re still there, just on the floor. The prophecy, however, ‘dissolved into nothing’ when the glass ball broke, so wouldn’t be recovered by Reparo.
Bellatrix's answer is correct, but I also wanted to add a more technical aspect - if an object in need of repair is magical, damaged very badly (i.e. it looks "beyond repair") or is very complex (like the human body), a spell to repair it may not exist or it would need to be specialized or very powerful.
We see this is magical healing - a broken arm can't be mended with a simple Reparo. Spells like Episkey are seen to heal broken noses and split lips, but more severe injuries need time, specialized potions, etc. to heal. Reparo worked on Harry's glasses on the train to Hogwarts, but I imagine the rubble of houses torn apart by earthquakes would need something more powerful than a mere charm.
In the same way, if we pretend for a moment that fixing the orb would somehow bring the prophecy back into it, as well, I think it would still require a more powerful spell. The orb is a magical object and therefore would be more complicated to fix; a simple charm probably wouldn't be enough.