There are five heavy kammas that give a definite result of rebirth in hell in the next existence — killing one's mother, one's father, an Arahant, injuring a Buddha, or causing a schism in the Sangha.
Hell is not permanent according to Buddhism, though it may seem like it for those reborn there. Eventually, the evil kamma that led to rebirth in hell expires and rebirth in other realms is then possible.
The cycle of births and deaths is eternal. Like all circles, it has no beginning or end. However, by practising the Buddha's teaching, the cycle of birth and death can be broken, and the end of suffering can be reached.
So the cycle of birth and death is without end, but not without any possible end. To put an end to death one must put an end to rebirth. Birth has a cause, which is attachment. Attachment has a cause, which is craving, and craving arises due to ignorance. By eradicating craving and ignorance, the cycle of birth and death can cease.