Why did hannibal win so many battles then lost the war?

Not sure. Didn't he push his men to much and by doing this he lose to many?

The war in Italy settled into a strategic stalemate. The Romans used the attritional strategy that Fabius had taught them, and which, they finally realized, was the only feasible means of defeating Hannibal. Indeed, Fabius received the name "Cunctator" ("the Delayer") because of his policy of not meeting Hannibal in open battle but through attrition. The Romans deprived Hannibal of a large-scale battle and instead assaulted his weakening army with multiple smaller armies in an attempt to both weary him and create unrest in his troops. For the next few years, Hannibal was forced to sustain a scorched earth policy and obtain local provisions for protracted and ineffectual operations throughout southern Italy.

Because the cunning Romans refused the opportunities to fight a decisive battle, meaning that any attempt to take Rome would have risked an attack from the rear. They knew that Hannibal had a limited campaign period before he would need to return to Carthage, all the time skirmishing to reduce the numbers and equipment of the Carthaginian troops.

Carthage didn't back him up much. His campaign was mainly a Barcid enterprise.

Why?....Because Hannibal had no 'siege engines'. He brought everything else with him (even war elephants). He beat the Romans in the field and just about every battle. But, once they retreated behind the stone walls of Rome he had literally no way to get in. He surrounded them of course, but the Romans had scorched all land around, all supplies/ food were inside the walls of Rome. Hannibal's troops starved without food/ supplies. Without siege machines he could not get over or breach stone walls. He could not have brought siege engines 2000 mi from Carthage and could not build them on site because the Romans had burned all the timber.

Not the best way to win....you lose your countryside, but keep your capital city and an army. It worked for Rome with Hannibal, and twice for Moscow against Napoleon and Hitler.

Yes unable to take the fortified Rome itself, the battles won turned out to be for nothing, but no one knew that while it was happening.