Stumbled across your question when I was troubleshooting something similar: 503 Service Unavailable for REST calls with ApEx Listener 2.0.2 DB 12c. My issues started in the RESTful services but I would also get a 503 error when trying to connect to the Listener via SQLDeveloper.
My problem was with the apex_al.xml and apex_rt.xml files generated by the java -jar apex.war setup process. Once I fixed them by hand the 503 errors in SQLDeveloper went away too.
Not sure if this is related to your problem?
Take a look at this post where I come clean on how a typo in the first pass of the java -jar apex.war setup process was the root of my problem: 503 Service Unavailable for REST calls with ApEx Listener 2.0.2 DB 12c
You'll see that I had the wrong connect string details inside of the xml files. Specifically the apex_listener/apex/defaults.xml file had the wrong value for <entry key="db.servicename">.
My first fix was to override it in the apex_listener/apex/conf/apex_al.xml and apex_listener/apex/conf/apex_rt.xml files. What I should have done is scrap my whole apex_listener directory and start over with the java -jar apex.war setup process, as that would have effectively fixed the typo I had in my apex_listener/apex/defaults.xml file.
Hope this is helpful,