[2022] Sanctuary Onslaught Elite recurring game freeze

Generally, a lack of connectivity to Warframe's game servers shouldn't cause the game to become unresponsive, you would just get errors when trying to submit your mission results.  It might give some clues if you leave the game running for a minute or so before killing the process (even if it doesn't look like it's doing anything), and then sending your EE.log file to the Support department.

You could also try closing the game using the Alt+F4 keyboard command. If it still responds to this, the game hasn't actually locked up which would be useful information