Verify you are using an Enterprise Database like DB2, Oracle, SQL Server or MySQL. Derby is strictly for demo purposes only.
Verify character set you are using for your external database, DevTest requires UTF-8 which is a 16-bit implementation.
Verify credentials being used to start the Enterprise Dashboard and Registry; not only must they be valid, but also have authority to Create, Read, Update and Delete tables as well as Alter on startup of both components.
Verify connection string. If you are sure your connection string is valid, use another JDBC database tool to connect to your database outside of DevTest. All DevTest components must be able to connect to the external database, so verify you can telnet to port the external database is running on.
Verify you are using the supported drivers. Other drivers like jtds are not supported even though they may work. The drivers specified to use in the local.properties and site.properties files is what you should be using.
Verify Schema. Enterprise Dashboard and Registry must each have their own schema. Follow the documentation as to supported databases and the recommended size for each.
Do regular Database Maintenance. Make sure your database has regular maintenance which includes checking for signs of corruption in the database, looking for problem areas, verifying it has all the required indexes (compare to DDL delivered with release), removing duplicate records, making sure database is not getting full and checking for any abnormalities in the database that might signal a problem. Run statistics regularly.
For further detail, add these properties to logging.properties file, they will show a more detail on the errors being incurred. Once your issue has been resolved, remove these properties.