This would require some changes to the REST services module.
In the javasource/restservices/publish/RestServiceHandler.java action there is a function called "processRequest" which ends with a "finally" statement in which the function rsr.dispose() is called.
This function performs a Core.logout action. If you remove the rsr.dispose() call the Logout would not be executed and the Session timeout should be used to clean up the session. If you only use a few users to consume the web service this could be worth considering, however if many different users consume this web service it might cause a lot of idle sessions in your application. And since objects with a reference to a session cannot be garbage collected this might have a detrimental effect on the application's memory usage.
You can change the default session timeout (10 minutes) by changing the custom setting: "SessionTimeout"