Just downloaded 220.127.116.11.78, Updated September 16, 2016 64 bit with JDK. Installed it on my co-workers computer. Opened the program and moved the mouse cursor over the + icon to add connection. SQL Developer closed. Tried several times, rebooted the computer, same behavior. I noticed that my co-worker was using Logitech M570 wireless trackball and wireless keyboard. I pulled out the wireless mouse/keyboard adapter from his PC and changed the mouse to wired mouse. Problem disappeared. I was able to create a connection. Switched the wireless trackball back and SQL Developer again started to close when I just hovered the cursor over the add connection icon. Is this a known bug?
Sometimes Java and a device driver (typically a video driver) do not play well together. Try starting sqldeveloper from a Cmd console window (...\sqldeveloper\sqldeveloper\bin\sqldeveloper.exe) and see if you get a JVM dump with a reference to the mouse driver. If so, attempt to find and install the latest version of the driver.