By default, <F4> opens the MixConsole 2, so I guess that you made a key command to use F4 as such, but which command does it actually trigger ?
Beside this, could you post a screenshot of the Audio System pane of your Studio>Studio Setup… window, just after the Cubase launch, this to see which driver is selected at this very moment ?
Beside this, if Cubase doesn’t shut down properly, it is likely that Cubase preferences aren’t updated in a reliable way. So, I would try to start Cubase in safe mode (<ctrl> + <shift> + <alt> when launching Cubase) and use the Disable program preferences option in the Safe Mode Dialog window, set the correct ASIO driver again and relaunch Cubase to see if this time, it is kept.