Does my Valheim server auto-save?
Currently, updated Valheim servers save the world files every 20 minutes from the previous 30 minute save interval. This was changed on the 02/15/2021 patch.
If you are added as an admin in your server, you can also force a save by typing save in the F5 Menu when you're in the server.
Knowledgebase: How to add yourself as an admin
Recovering Lost World Files:
It's confirmed that renaming WORLDNAME.db.old to the current WORLDNAME.db and removing the newest world file is a viable option for corrupted/deleted worlds, to save at least some progress. For the time being there are no fix to corrupted worlds, except from backups.