You can see Database Agent events on the Database Monitoring > Events window and in the <agent_home>/logs/db-agent#.log files. Database Agent events are of type Agent Diagnostic Event, with case-specific messages attached.
Agent Diagnostic Events
Initialize/re-initialize the DB collector
Summary: Initialize/re-initialize the DB collector
Description: Sent when database collector has successfully started. This happens when you configure a new collector, start/restart the agent process (in which case you'll see this event once for each collector), or when the collector recovers from a failure to communicate with the monitored database (for example, when the database goes down for a while, then comes back).
Initialize/re-intialize the hardware metric collector
Summary: Initialize/re-intialize the hardware metric collector
Description: Same as the above, but refers to a hardware collector, not a database collector.
Server parameter [?] has been changed from [?] to [?]
Summary: Server parameter [?] has been changed from [?] to [?]
Description: The Database Agent constantly monitors database configuration parameters. When a parameter changes, which generally means a database administrator made a deliberate change, the agent sends this event. AppDynamics Database Visibility users can use these events to track configuration changes in their databases.
JDBC Driver-related Agent Diagnostic Events
Summary: The text of the message is the error from the vendor's JDBC driver.
Description: When the agent fails to collect data from a monitored database, it sends this event, and goes into sleep mode for one minute. It will then retry contacting the database every minute until it succeeds. Once it succeeds, it will send an Agent Event "initialize/re-initialize" message, as described above. This happens when the database goes down, or when you add a collector with a wrong password, or wrong hostname, etc.
When the Collector is in sleep mode because of an error, you'll see an indicator next to the database on the Infrastructure and Infrastructure > Databases, on Configure > Collectors window. You will also see the full text of the error in the Infrastructure > Events window.