SQL Developer doesn't disconnect anyone from the database unless they ask to quit the connection.
What you're seeing are network timeouts, or a database resource consumer group plan killing idle sessions.
Try fixing the issue at the source - but you'll have to find out why the connections are dying first.
Also, when I upgraded SQL Developer it removed it.
The extension framework used by Sql Developer was upgraded for 4+ and is NOT compatible with the previous framework.
No extensions written for previous versions of sql developer will work in the 4+ version; they need to be modified for the new framework.
That extension developer has modified their extension for sql developer 4+ so if you insist on subverting your org's security check their website and download/try that new extension.
As Jeff already told you any 'disconnect' is a network or DB issue and will usually ONLY occur for connections that have been idle (i.e. unused) for a lengthy period of time (such as someone going to lunch and leaving their apps open).
I also suggest that you FIRST research the actual reason developers are having idle connections for extended periods of time. Leaving such connections open when the developer is not present and actually using the machine is a security risk.
Disconnects can also occur if a user launches a process that executes on the server for an extended period of time before contacting the client machine again. That would be the ONLY acceptable use, IMHO, for such a 'keep alive' extension.