Well, this is part of the reason why I think puzzles often are at war with stories; if your game gets the player stuck (let’s say that a puzzle is something that’s likely to get a player stuck for a little while) then it brings the story to a halt. But I’m not sure this is unique to text adventures; it’s a question of how good you are at dealing with the mechanics. It disrupts my immersion in Cave Story’s story just as much when I have to replay a boss fight for the twentieth time as it disrupts my immersion in Sparrow’s Song when I can’t get past the nymph.* And with IF, at least a well-designed hint system (or failing that a working walkthrough) will get you past the obstruction. In action games, if your reflexes aren’t good enough you’re SOL.
Not that I’m saying that this is an answer to your question, just that other games can do very well at recreating the “watching a movie that stopped on me” feeling.
*Well, in Cave Story I get the hint of a bit of progress and in Sparrow’s Song I don’t. But Sparrow’s Song may be out on the extreme of unclued puzzles.