I'm playing through on Classic Ironman and it's been seriously tough so far. I've got my third best squad (please don't ask about the other two, it's still a sensitive matter) to the start of the temple assault, but haven't yet started it as I'm not sure what will happen if I fail. Is it totally game over? Or do I get the chance to train up a new squad a try again?
Ok - in the interest of science I have tested this out fully. You will always be given a 'restart mission' option if your volunteer dies.
I have tested this on the following difficulties;
They all give you a 'restart mission' choice. The non ironman also gives you a 'load last save game' option.
As other people have reported, some people think they have seen a "game over" message when you fail, myself included. I suspected this answer might have changed after the first patch, where they made some changes.