Trigon: Space Story makes it easy to forget that your crew has feelings. Morale is briefly mentioned in the tutorial and is affected by your many encounters and battles. The best thing to do is to keep your Morale high enough that crew members won't leave.
How to keep Morale high in Trigon
To keep Morale high, you have to focus on keeping your crew safe. When fires start on the ship, don't have crew members put them out. Make a path from outside the ship to the fire to suffocate the fire. Always have 35 food in your storage at all times, and make sure to spend the points to upgrade your oxygen for extra food production.
If your Morale is low, crew members will complain and mention that they wish they had died after battles are over. Taking a day to repair the ship at a station will give the crew's Morale a small boost if there is enough food to feed them.
In the worst case scenario, get a cryo chamber and freeze a squad mate when they threaten to leave. You can sell them to a station and find a new crew member. It's a bit mean, but at least you'll get something instead of losing someone outright.
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.