The error you are getting would imply that the database server was being shut down during the update, which is a standard procedure since the built-in database is sometimes patched. Please open "Services" on this host and locate the "EventSentry Database" service - is the service running? If it's not, please start it. Please note that EventSentry does not install a MySQL database, the database which ships with EventSentry is a PostgreSQL-based database.
In regards to the Heartbeat service not updating, in the management console please click on "Heartbeat" and then click the "Update ..." button on the bottom left. When prompted, browse to the EventSentry installation directory, usually C:\Program Files (x86)\EventSentry. This will copy the eventsentry_hb_svc.exe to the C:\Windows\syswow64\eventsentry directory.
If the EventSentry Database service was stopped then we'd definitely want to investigate this further, this service should always restart automatically when you apply a patch.