I'm about 5 hours into the game and lost every single named/class soldier. I have 6 soldiers left, all at starting level. Is it even worth me carrying on this save?

I was doing a basic mission, kill a few guys, dont die. Except my guys missed the kill a few guys bit which let to them not doing the dont die bit. My best sniper who was almost max level missed every shot during the entire level, nearly always above 50% with a few at 80+%, which led to her dying. Once she died, the rest wasted since they were on the front line.

Shall I just restart? I quit the game straight after out of rage and cant be bothered to play if I'm gonna lose every level with some shit soldiers.

The game is hard and shit like this happens, but the metagame is balanced in such a way to account for it, you can nearly always recover with careful planning from this point onwards.

Terror missions might be a bitch and you may get a low rating on the council report, but its still possible

I was in a situation like that and then had 2 terror missions in a row come up. At that point I went ahead and just scanned till I lost to see the bad ending.

I thought I was in a lose condition since I was lategame in Ironman Classic, every soldier died, and, even with the Squaddie perk, I lost like five or six straight missions. Now I'm kicking ass and progressing toward endgame.

Sometimes you're in a death spiral, except when you're not. I don't know what your base/finances is like.