On a DB failure, a WL JDBC store service will make a brief attempt to reconnect before shutting itself down along with any services that depend on the store.
It isn't necessary to restart the entire WebLogic Server JVM to bring the affected service(s) back if you can use the Automatic Service Migration feature. ASM can automatically restart a failed service on a different WL Server in the same cluster, and/or can try a restart-in-place for the service if the service's original host WL Server JVM is still running. The Automatic Service Migration (pdf) white-paper has a thorough discussion of this area.
In addition to ASM, there's also a "whole server migration" option that can automatically restart or migrate an entire WL server.