Databases do not run away by its own and you can only restore, if you have made a backup before.
If you have made your backup using the web database manager interface, you should have a zip-File stored locally to upload, when you want to restore your database using the web database manager. If you did make your backup using postgres, you should have a dump-File, which you could restore using postgres (and not using the web database manager).
As mentioned by Ray, check your postgres databases. If it disappeared, check who has deleted it how. Do a restore using the corresponding method (web database manager or postgres).
If the database is available in postgres, you may check the following reasons for Odoo not finding the database:
- ownership/access rights as mentioned by Ray
- if you are using dbfilter or the module dbfilter_from_header, check the configuration/settings
- if you are using a proxy server, check the configuration/settings
If Odoo is showing that screen, then it can't find the database. Check PostgreSQL in case the owner of the database changed.