ORA-16820: Fast-Start Failover observer is no longer observing this database

One obvious possibility is the observer does not connect to the database again after the database restarted. In this case, restart the observer will solve the problem.

Below is another possibility apply to 10gR2. (MOS ID 730379.1)

Applies to:
Oracle Server - Enterprise Edition - Version: 10.2.0.1 to 10.2.0.4
Information in this document applies to any platform.
Goal
The Primary Database locked up or hangs (i.e. allows no connections)

The Observer stopped monitoring it with this Error Message:
" RSM0: HEALTH CHECK ERROR: ORA-16820: Fast-Start Failover observer is no longer observing this database "

Primary Database is hanging but not down, so no Fast-Start Failover was initiated although the Observer could not reach the Primary Database anymore.
Solution
In 10.2.0.x, Fast-Start Failover is only initiated if the Primary Database is not available because it is down. Here the Primary Database was locked. The Observer considered it as not reachable but still available, ie. the
Primary Database is not down. So no Fast-Start Failover was initiated.

This has been changed with Oracle 11.x where we can setup several Conditions (also User-defined) to initiate a Fast-Start Failover to handle such Cases, too.