Just to make sure, please check the Settings -> About tab to make sure the 3.35 were installed properly. Happened to me two days ago that I thought I had updated the Firewire drivers just to find out I did not (must have clicked something wrong at some point).
What's strange about your issues is that normally the RME drivers load even when no interface is connected and allow the interface to be turned off/on even while a DAW is loaded. Please try the following two things:
Delete/Rename Live's Preferences.cfg as it can get corrupted:
https://www.ableton.com/de/articles/corrupt-prefs/
When the error happens keep Live running, go to Windows' Device-Manager and try to disable the AIO. Does it ask you to restart or does it disable right away? Does Live recognize it when you re-enable it?
Do you use the AIO for Windows system sounds?