Please let me know the reasons of release upgrade failure in PostgreSQL which you guys faced while doing it.
Example: 9.5.1 to 9.5.2
It is highly unlikely that you will encounter a failure when upgrading to a new minor release.
Major releases are a different matter though usually the upgrade happens just fine but if you aren't careful to also update your applications they could start working if you are using features that have changed incompatibly, though we do try to minimize that.