Note that I had months of successful missions, including terror ones, and had three successful turns on this mission before this problem occurred.
The game doesn't leave the "Hidden Movement" phase, as if some alien was thinking indefinitely.
I can still press Escape and have the menu, or hear sounds when I click.
Leaving game and resuming the save game (which is on ironman mode) reproduces the problem 100 % of the time on this computer. Save game would be attached if I had permission to put attachments here!