I'm not exactly sure. There are games that I thought immersive originally but which had that feeling slowly degrade. Call of Cthulu: Dark Corners of the Earth, for example, is highly immersive for the first portion of the game. Then you get a gun and everything stops being scary. You can actually eliminate the element of fear at that point, your character stops being helpless and, most immersion-breaking, your characters injuries, which pile up rather quickly at that point in the game, despite requiring sutures and bandages and what-have-you, still are entirely solved after applying whatever healing equipment to them. Normally this wouldn't be a problem for me, but in a game that had, up to that point, been so immersive, it completely broke that illusion for me.
Other games I feel could be immersive if I didn't feel the need to look at guides due to the overwhelming obscurity of all the extras in the game. That's kind of how I feel with Dark Souls, right now. I love the game, and I'd be totally into the mythology and world, if it weren't for the desire to not die coming along and making me check the wiki for item locations almost every session. That, of course, is my fault.
I suppose stealth games tend to be what I find most immersive. There is an intensity there that isn't in other games. That moment of "Oh SHIT, oh shit, gotta hide" is something that I don't get anywhere else, and provides genuine adrenaline, for me.