It is rather uncommon to use Jenkins as a service health monitor, but you might perform each of your checks as a JUnit test, write the results as a JUnit file, then show the results as a JUnit test. If a service is unavailable, the JUnit results will show as a test failure.
If that's not a comfortable technique, you might consider creating a multi-configuration job with one of the axes of the configurations being the names of the servers you're checking. A failure of one of those jobs would be your indication that the service is not responding.
Mark Waite