This code ought to at least log subclasses of Error (OOMEs in particular). Without doing so, there is no way to know that the JVM "got sick" when executing this thread. Even though the thread itself likely (I didn't evaluate the control paths) continues to behave correctly, I like to know if my JVMs are having issues.

} catch (Throwable t) {
   averageRoundTripTime.reset();
   currentServerDescription = getConnectingServerDescription(t);
}