How do you manage databases in development, test, and production?
Your developers need to write change scripts (schema and data change) for each bug/feature they work on, not just simply dump the entire database into source control. These scripts will upgrade the current production database to the new version in development.
Your build process can restore a copy of the production database into an appropriate environment and run all the scripts from source control on it, which will update the database to the current version. We do this on a daily basis to make sure all the scripts run correctly.
There are a couple of good options. I wouldn't use the "restore a backup" strategy.
Script all your schema changes, and have your CI server run those scripts on the database. Have a version table to keep track of the current database version, and only execute the scripts if they are for a newer version.
Use a migration solution. These solutions vary by language, but for .NET I use Migrator.NET. This allows you to version your database and move up and down between versions. Your schema is specified in C# code.