While Kushina gave birth to Naruto, Tobi came in and used her weakness to extract the Kyuubi. That was the first shown event, where a Jinchuriki survived the extraction of the tailed beast. How could Kushina survive that?
Kushina survived the bijuu extraction due to the Uzumaki clan's incredibly strong life force.
One trait of the clan is that they have immense amounts of chakra in their reserves and are unrivaled when it comes to sealing techniques; as shown by Minato Namikaze who was taught by Kushina Uzumaki, his wife. They also were known for their extremely long lives and will to do what they need to do. such that they can even survived after the extraction on which gaara wasnt able to do when the shukaku was extracted from him.
The members of this clan possess incredible longevity and vitality seemingly inherited from their Senju ancestry. One notable case is that of Mito Uzumaki, who lived from before the founding of Konoha, to well into the term of the Third Hokage's reign. This vitality was the reason Kushina survived the extraction of her tailed beast, though she was greatly weakened.