My WordPress installation offers mean update to 3.9.
I click on Update now and the update process is started and finishes successfully.
However, then I am still presented with the same update screen. It seems that the update is not applied for some reasons. Any ideas?
After you run the upgrade from within the wordpress admin, restart your application, either using rhc app restart command, or click the restart button in the web console, then it will tell you that a database upgrade is required. Click the button and everything should be upgraded to wordpress 3.9.