Survive means manage to keep going in difficult circumstances. In some ways I feel like this is quite a mundane definition, almost boring: it doesn’t capture the flavour of what people tend to think about survival. Over time we have skewed survive to only mean situations where life is threatened and nearly all hope is lost.
Survive implies, I think, a challenge that is being worked through. It feels like the best verb to describe the kind of challenge being overcome in the PhD viva: it’s not a new challenge, it’s not impossible, it’s not supposed to be a struggle. It applies to the PhD as well, of course, though the challenge is bigger, for longer and can take many forms.
Manage to keep going in difficult circumstances sometimes doesn’t capture the nuance of the difficulty or the challenge. It doesn’t account for how someone might feel about their PhD or viva. It’s still the best verb I can think of for describing how someone can engage with the circumstances of their viva.