I upgraded Oracle SQL Developer from 220.127.116.11 to 18.104.22.168, just for the heck of it. Unfortunately, all my saved connections had disappeared! After a text search I found the connections are stored in a file called IDEConnections.xml under the folder sqldeveloper\jdev\system\oracle.onlinedb.22.214.171.124.25. I copied this across to a new folder that had been created (oracle.onlinedb.126.96.36.199.36) and bingo they’re back again.
Bonus – now I know what file to back up if I want to restore my connections later on.