Why didn't the senate of Carthage reinforce Hannibal in Italy?

No, Hasdruabal went, not by the order of Carthage, but because Hasdruabal and Hannibal were talking and making their own agenda on how to win the war behind the Carthaginians backs. Hannibal and Hasdruabal were both loyal to Carthage but realized Carthage was not as into this war as they were due to their long-standing hate of Rome, and decided to win on their own terms. It might have worked if Hasdrubal was not cut off as Hannibal was only 2 miles away from Rome lying in wait.

Carthage did not send more troops to Hannibal because Hannibal had failed to secure a port for the Carthaginian reinforcements to dock in. This, coupled with the tiring of Hannibal and the Carthaginians resulted in defeat.

Also, in addition to my previous answer, Hannibal was never allowed to capitalize off of his battle at Cannae as every time he flipped the allegiance of a Roman city, Rome would follow and flip the allegiance back. Also, Rome employed a famous strategy of avoiding conflict with the Carthaginians led by Hannibal which, coupled with Carthage's inability to help, led to Hannibal's forces being "stuck" in Italy. Many historians are perplexed at why, when Hannibal was at his highest power, immediately following Cannae, he did not march for Rome. We may never know if Hannibal could have taken Rome if he chose to at this time. But, over time, Rome slowly gained the upper hand and soon Hannibal was too weak to strike for Rome, even when he wanted to.

Carthage’s Senate never wanted to send reinforcements to Hannibal.
There - I said it.

At the least, they were never sufficiently motivated to do so.

There was a strong contingent in its Senate opposed to war with Rome. Some even claim they were bribed by Rome to dissuade them (based on cryptic language in letters between Roman Senators). This can likely never be proven or disproven.

Those aligned against the Barca faction preferred instead to give all overseas trading posts and ports to Rome or Greece or whomever, and to expand farming and pastoral developments on the African continent — which itself would have led to large scale conflict with long-term allied Berber tribes on whose land they would have encroached. In that conflict, Carthage would have been easily outnumbered, deprived of its Numidian cavalry, and would likely have ended no differently for Carthage empire, culture, and society.

Carthage did send some troops to Hannibal in Italy, just not very many. I remember reading that ships did make it into either Tarentum or Lucri but I am having trouble finding the original source I read that from. I was able to find these sources below:

" In Italy, Carthage finally sent at least a small force of reinforcements that joined Hannibal at Lucri." (1)

" Therefore, he turned his attention to southern Italy, where he captured Tarentum and several other ports (213), facilitating the supply of new soldiers from Macedonia and Carthage." (2)

"...Carthaginian authorities... sent reinforcements and subsidies to Hannibal in Italy, and to Mago in Spain, with orders to rekindle the war..." (3)

1. http://www.unrv.com/empire/after-cannae.php
2. http://www.livius.org/articles/person/hannibal-3-barca/
3. http://www.ellopos.net/elpenor/rome/3-06-war-hannibal-cannae-zama.asp?pg=76

They did send more aid. Hasdrubal, Hannibal's brother, came with a whole new army which miraculously made it all the Italy, but then was unfortunately wiped out at the Battle of the Metaurus.

It comes down to two issues: no army to send and no navy to get it there.

The war of Hannibal and the Barcas against Rome was more or less a personal project by that family, who controlled Spain and its resources and built up their armies there. Hannibal's initial thrust across the Alps and into Italy needed to be done because Rome had complete control of the seas.

Rome sent the forces intended to stop Hannibal in Gaul on to Spain, and raised new forces to fight him in Italy. They faced Hannibal's brother Hasdrubal there for some years.

In Carthage proper, there were essentially no troops at all. There was also not much of a navy, or shipping to carry troops to Italy. So when Hannibal's march ended up in essentially a stalemate, there was no way to get more than a trickle of help through the blockade, although it was a constant concern, especially when King Philip of Macedon allied with Hannibal.

After some years, Hannibal's brother faced a deteriorating situation in Spain himself and marched to join Hannibal, as while he had an army there was no other way to get to Italy. He was caught and his army destroyed by the consuls of the year in North Italy.

When Scipio Africanus invaded Africa some years later, there was still no real army in Africa to face him. Hannibal had to be recalled for the final battle at Zama.