Log messages when an item check fails look like this :

JMX agent item "jmx["jboss:service=WebService","State",10019]" on host "test" failed: first network error, wait for 15 seconds

When the host is declared available again, they look like this :

enabling JMX agent checks on host "test": host became available

Notice how the item key is not identified in the latter case.
While knowing the failing key is important, it is also often useful to know which key succeeded (for example, if there are multiple jvms on the same host).

Would be good to add the successful item key in this log message as well.