I have played “Where the Sun Sets” main mission, and it is marked as completed, all 3 objects.
But next time I start the game, that mission is restarting, and it looks like I just installed the new DLC.
When turning off the game, I always first go to a safe house, then exit to main menu and then exit to desktop.
I always make sure to open the Plundra (stash box) to force a game-save before quitting.
I belive the game saves on mission completion as well so this definitely sounds like a bug, not just another user error.
Out of curiosity, does your backpack keep any changes, newly aquired items and/or remember your discarded items/used ammo and so on?
If your inventory gets reset too then there may be some issue with write permissions on your harddrive.