According to Jon Thatcher's DevCon presentation, you can store the encryption password using the Admin Console the first time you open the database. It's referred to as the "keystore". The server then uses this information to open the database on restart.
John May wrote:
Am I correct in thinking it's not possible to auto-open encrypted databases on server startup? This seems to be a pretty big ability to be missing...
Mike Mitchell is correct. The encryption password is only challenged when either FileMaker Pro, FileMaker Go or FileMaker Server open the file locally. A client accessing a hosted encrypted file will not be challenged for the encryption password, since the file has already been opened on the hosting side.
See more information here...