You'll need to make sure your game is saved in The Ascent before quitting. Some of the missions can go on for a while, and losing progress could be frustrating to say the least. The save system in The Ascent is slightly different to what you might expect. Here's how to save.
Read More: The Ascent Review
The Ascent Game: How to Save
To save in The Ascent you will need to reach designated autosave checkpoints. These are fairly frequent, and you'll see a save logo onscreen when it happens. If you want to check how long it's been since your last save, go to quit the game. Before you confirm, you'll see a message describing how long it's been since the last autosave.
Can You Save Manually?
You cannot save manually in The Ascent. You can only save your progress by reaching checkpoints. Given that autosave-only has been prominent in the pre-release items we've had on the game, this is unlikely to change. Just make sure to check your progress before quitting.