Is there something built into this, that if the proxy server cannot be reached, it simply tries again but bypasses the proxy on this retry?
Yes.
I was surprised to see this, but here it is in the source of the internal connection: sun.net.www.protocol.http.HttpURLConnection. On line 760, if we've tried all the available proxies and failed to connect, we try a non-proxied connection.
Am I searching wrong somehow?
Maybe. Right or wrong, the Java philosophy seems to be that system properties are ad-hoc things and the only way to know that one exists is to read the documentation for the thing that it affects. In this case, HttpURLConnection links to a page on Networking Properties.