So you basically want cataphracts riding over the legions, is that it?
Why don't you think the Romans would adapt and innovate against such a threat? After all, when the Punic War started Rome basically had no navy at all yet it reversed engineered a wrecked Carthaginian ship, added the corvus to the design, built several fleets, lost more sea battles than it won, learned from the battles it lost, and went to win all three wars on both land and sea.
The question here just isn't whether Carthage develops cataphracts but whether Rome becomes stupid.
Actually I think Hannibal's elite Iberian cavalry was very heavily armored. Covered in chain mail, or something. Ah, here's a description:
The Iberian heavy cavalry was what hannibal had with him at Cannae. They were (obviously) far superior to the Roman cavalry of the time, made more so by their status as a western sort of very heavy cavalry (think cataphractarii) with barded horses and high quality mail or scale armor. Their only handicap was the smaller spear and shield they carried.
Also there was another group of elite troops back at Carthage called the sacred band:
The Sacred Band of Astarte was a cavalry unit that wore iron armor and carried a 3.5m lance. They fought in the Greco-steppe manner with a two handed lance. Their horses were barded with iron lamellar. Their horses were a mix of the african (arabian) breed and the andalusian (iberian) breed. They were on a par with Hetairoi or Granpavar (elite) cataphracts, but were trained from birth as property of the temple. A predecessor of the Mamluk, essentially, but from the second and third sons of noble families.
They were held back at the battle of zama by hannibal's political enemies though.
http://forums.totalwar.org/vb/archive/index.php/t-44039.html Where I copied those descriptions. Sorry i can't do better at this hour.
So yeah, Carthage had super heavy horsemen which were well used in the hands of at least Hannibal. Really if you want a TL where Carthage challenges rome longer, your best bet is probably a change in Carthaginian politics. Say the sacred band are not held back at the battle of zama and go on to crush the roman cavalry. Then they come from behind and ruin the roman's day.