I'm sorry, but losing progress and having to redo things is just plain tedious bullshit. Unless you happen to be a masochist *cough* Dark Souls fans *cough*, than that just isn't fun.
Depends on what you call fun. For me, games without tension aren't fun. That goes triple for horror games, but it applies to any game. I think that the purpose of a game is to overcome some sort of adversity and accomplish something. There's no reward without risk, and the tension and accomplishment you feel from that kind of game is great. Which is why many people love Dark Souls... it's not because they're masochists, it's because it feels great to play a game where winning actually means something.
But then again, there are those who aren't very interested in the "game" aspect of games, and tend to see games more as experiences. For that type of person, I guess losing progress gets in the way of your experience. I guess you must be that type.
I personally think that video games should strive to do both, which is why a lot of people see Dark Souls as the best game of this generation... it excels both as a game, and as an experience. Anyway, I believe it makes sense for horror games to follow that template, at least a little bit... they don't have to be as punishing as Dark Souls, but they shouldn't be afraid to make the player face some risks. That source of tension is way too valuable for a horror game to just ignore it.