First, Carthage wasn't exactly happy with Hannibal starting a war with Rome. They'd already lost one war. The Barca family also had political enemies in Carthage. However, after the battle of Cannae, they authorized reinforcements to be sent, the only time Hannibal would receive reinforcements.

The big problem for Carthage is they were heavily reliant on Iberian mercenaries to provide those reinforcements. And Rome had decided to fight it's offensive campaign not in Italy against Hannibal, but in Iberia, against Hannibal's brother Hasdrubal. In 215 BC, Hasdrubal had gotten some reinforcements, and was attempting to march north and around to reinforce Hannibal. At Dertosa, he tried to repeat the tactics Hannibal had used at Cannae, but his center collapsed before the flanks could win, and his infantry fled. That disaster meant Carthage had to send the bulk of the reinforcements that Carthage had intended for Hannibal to Iberia instead.

Hasdrubal was forced, in 213/212 BC, to deal with a revolt in Numidia. The Carthaginians slowly lost ground in Iberia until finally Hasdrubal pulled out entirely and attempted follow his brother's path into Italy and join him. He actually made it across the Alps, but was defeated by the Romans before he could join his brother.

To summarize, Hannibal was holding his own in Italy, and Carthage did not have enough troops to reinforce both Hannibal and Hasdrubal in Iberia.