Before The Last Jedi
It appears that Captain Phasma has indeed survived.
As this article says,
But according to the L.A. Times, Captain Phasma will also appear in Episode VIII – in other words, whatever happens in this episode, Captain Phasma won’t be killed.
“She’s an important character, a baddie in the best sense of the word,” Lucasfilm President Kathleen Kennedy confirmed, without revealing what Captain Phasma will be up to in Episode VIII, which is set to debut in 2017.
The original Los Angeles Times article can be found here:
But you won't see Phasma tapping out after being carelessly knocked into a sarlacc pit like a wobbly toddler. Kennedy has big plans for Phasma and confirmed that the captain will carry on into the next movie. "She's an important character, a baddie in the best sense of the word."
Phasma, or the Chrometrooper as fans have dubbed her because of the custom silver armor she wears as a sign of her authority, commands the Stormtroopers of the First Order. But it wasn't talk of villains that intrigued Christie, rather Kennedy's thoughts on the status of female heroes.
"Kathleen Kennedy said to me, 'Have you ever Googled 'female heroines'? I said, 'No,' and she did it for me. If you do it, there are a lot of scantily clad women. Now women should be allowed to dress exactly however they choose, but the idea that you Google female heroines and there isn't a diverse range of examples that come up, I find it a bit depressing."
In an interview, J. J. Abrams revealed nothing about Phasma's role in future films, save that Christie is his "favorite [actor]".
The Last Jedi
With the release of Episode VIII in December 2017, we see Captain Phasma return, albeit briefly (so she's alive!). After Rose and Finn, along with DJ, sneak onto Snoke's flagship,
They are captured by soldiers, and eventually brought before Captain Phasma and her stormtroopers. DJ betrays the Resistance, and Rose and Finn are about to be executed by Phasma, before Vice Admiral Holdo rams the flagship.
In the ensuing chaos, Finn battles Phasma in single combat, and eventually
Finn defeats her. The floor underneath Captain Phasma gives way, and she falls into the fireball beneath.
Any role Phasma may play in Episode IX is currently speculative for those of us not in the know. I can get back to you on whether or not she survives in approximately 2 years.