I think it could work but only in very specific situations, e.g. a shortish game that is specifically geared towards re-playability. Look at something like Laura Bow
which is full of bits you can and will miss on the first play through, yet it works because
1) The player expects to have to play the game several times
2) There is always a 'proper' ending
3) You get hints on how to do better when you reach the end
By 'proper' ending I mean you don't suddenly get killed 2 hours in because you didn't pick up some item in the first 10 minutes. You can get to the end of the story without taking the item, but you won't get the best ending.
In other words missing items are fine as long as...
1) The player understands that the game works this way and that they are expected to (and not severely punished for) miss things and have to replay. Also this isn't a one off instance, the whole game is structured around re-playability.
2) You can get a satisfactory ending without finding the item. The player doesn't get a sudden 'You didn't have item x so you died' and the player is never left at a point where they can't move any further.
3) The ending leaves the player with something to work on. If they rescued the princess but she's sad because you forgot her teddy bear then next time you should work out how to get the teddy bear before leaving the castle. It should be obvious what the player needs to do to get a better score.
Also don't forget about autosaving...