Trigon: Space Story does not tell you when it will save, so it's hard to know if things will work out if you leave. This is because there is no conventional save system, and there is no way to save manually. Each auto-save is overwritten at the start of every day.
This means that if you start a new day in Trigon: Space Story and make a lot of progress, you'll lose all of that progress if you don't do something to make the day go by. If you die, you lose your one save, so it's imperative that you take each playthrough seriously. This doesn't mean there isn't a way to cheat the system, however.
Related: Do I lose crew on enemy ships when they explode in Trigon: Space Story?
Are there checkpoint saves in Trigon: Space Story?
Every new day is saved, meaning that you're given a checkpoint each day. When you know you're dying or you lose an essential crewmate, you can always Alt+F4 out of the game and try again from your daily save. While this is not the way the game was meant to be played, it's a nice way to lower the difficulty if you don't like perma-death in Trigon: Space Story.
For more on Trigon: Space Story, check out What's the difference between Trigon: Space Story and FTL? or Is there multiplayer or co-op in Trigon: Space Story? here on Pro Game Guides.