Does Hellblade: Senua's Sacrifice delete your save file if you die too often?

The short answer is, in practice, no, your save won't be deleted. I intentionally died many, MANY times (in the hundreds) without my save being deleted. Some stuff went down, but I didn't lose my progress. Of course, it's possibly that if I had died a few more times my save would have been deleted, but I hit a point where the game seemed to be telling me that everything that was going to happen had already happened.

The long answer is, the game straight up tells you, in quite literally the only popup all game, and very early on, that your save will be deleted if you die too much. There were no review codes given out, so when reviewers hit this point, they went "oh dang better tweet this." Totally understandable. It never occurred to most of them that the game might be lying, and they might have felt a sense of responsibility to their audience. They reported what the game told them. It just seems that, like so many other times, the game was lying.