Assuming you are using Windows, the installation path steam uses for StarMade is protected.
Since the universes are saved within the install's location, it may happen, that the game cannot save due to lacking permissions.
To solve this problem, change the installation's path in the StarMade launcher. You can access the setting by clicking "Installation Settings" in the options menu in the launcher.
Set the path to somewhere you have readwrite access to(e.g. "C:\StarMade\").
If the problem still occurs, permissions weren't the cause to begin with, and you'll likely need to either look at other solutions, or submit a support ticket.