Short Answer:
Have something more valuable than the item that the player can lose if they hesitate to use the item. EG You might use your single-use invincibility potion to save you from death in a game where death is permanent.
Long Answer:
I think the only games in which such an item can work are ones where there is some form of persistent punishment for failure: Things like permadeath, loss of money/exp/stats on death, limited lives before having to restart the game (that's pretty outdated, but whatever). So when the player gets stuck or comes up against a challenge that they are likely to fail, they have an incentive to skip part or all of this challenge using the super item.
You could look at a lot of old arcade shooters, where you where often given about 3 bombs to use per life and could not recover any more. Bombs where valuable, but not as valuable as lives. Players would never use them unless it was necessary, but they wouldn't hesitate if they thought it would prevent them from dying. The same principle can be applied to single-use items, as long as there is something more valuable that the use of such an item can protect.
In a lot of games, failure is not really penalized and therefore there is no reason to use rare resources. There is no reason to use limited resources to prevent the loss of a life when you have infinite lives. I suppose you could add a particular encounter to the game that forces the items use (like the Master Ball in pokemon), but that can fall into guide dang it territory.
Making the game more difficult is not a solution, as players will not have the item for the vast majority of their playtime. "If this is hard now, I should save the super-weapon for when it's even worse!"
EDIT: As zzzzBov points out below, you could also make the item itself disappear upon death. Which would certainly make players more likely to use it.