Just to confirm, I did read that saving while combat is not allowed because that has been decided. period.
However, I would like to propose "save and quit" save slot with "continue current game" button when you come back to game, which saves game and quits at any point of game.
I just got a base under attack - mission and it took me about ten times more time to find and eliminate all the aliens than usual ufo battle, and it started to get way too time consuming. I just walked around in my base for nearly a hour before I found the last few aliens. I didn't have much time so I considered to just plain quit and load situation 24 hours (game time) earlier. This is a issue which just plain has to be fixed, if not immediately then some point in future. Game with unplayable missions because real life limitations is broken IMO. If someone abuses that by making backups of that savegame I say let them do that. It's cheating, but you can also cheat by modding the game so that your characters are basically invulnerable easily enough anyway.
Other way to fix that is to ensure that there is no such long lasting missions. In my above case my soldiers spawned almost as far as it was possible from the enter points of the base and they had no idea where the aliens were. Some sort of motion detection system to alert where aliens have been detected has to be implemented. Maybe add entity "motion detector" which works as "civilian" target for aliens in corridors. When alien attacks that you might then lose the knowledge of the alien activity in that area, but you know that there has been alien in there. Haven't played game long enough to know if there are other such missions (like alien base missions in x-com), but if there is and speeding up them becomes too hard this "save and quit" becomes necessity.
If it is technically difficult, then just put it on to-do -list until someone has time to implement it. Because game is in "work in progress" -stage it doesn't matter much if that is not done this instant, but it needs to be done.