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like permadeath, loss of money/exp/stats on death, limited lives before having to restart the game (that's pretty outdated, but whatever).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.

How to prevent the "Too awesome to use" syndrome
I am a graduate student in math in my final year, and for several years have been teaching at my department as a lecturer. This semester, in the same lecture hall there is another lecture that starts 20 minutes after my class ends. It's taught by another instructor from my department. I usually have many students coming to office hours and there are also students asking questions immediately after lecture. Due to other activities, I cannot have office hours right after the lecture this semester and can only stay for about 15 minutes to answer questions.

Many times in the past I had a similar situation and never had any issues with it. This semester the instructor who is teaching right after often arrives 20-15 minutes before her class starts and tells me immediately that I have to go with my students somewhere else. 

I make sure to leave the blackboard clean and take all my stuff away from the instructor's desk before she arrives, but I do believe that I have a right to stay in the classroom after my lecture for at least 5-10 minutes. There is no vacant classroom around, and I don't have time to go with students to my office, which is in a different building.

Last time the instructor told me in front of my students that I don't understand "simple things" and that I am "playing games". When I was talking to one of my students, she stood very close to us and clearly demonstrated that she wanted us out. I tried to explain her that I couldn't go anywhere else due to my time constraints, but she didn't want to listen to me. I really don't understand what "simple" things she meant and what "games" I am playing. 

We leave the board clean. She doesn't need to set up a projector. She can still talk to her students before her class starts, if she wants to (even though it seems like her students don't ask her any questions before their class). So, I don't see how I cause any disruption. 

I had met this woman many times before this semester, but we never talked. I didn't see her talking to other instructors/students much, and she seems to be quite reserved and a bit neurotic. She doesn't want to have any conversation with me regarding the issue.

I felt really offended after last class when she said those things to me in front of my students. What would you do in my case? 

Added later: There are no official rules regarding classroom occupancy between classes. Instructors are supposed to use common sense and be reasonable. For me using 50% of the break time seems reasonable to answer questions after lecture seems reasonable. I agree that for some people it may not.

I don't block the entrance to the classroom. A few students from the next class who come earlier always go ahead and take their seats as soon as my students start leaving the room. I also had one of the students from the next class listening to my explanation to one of those after-class questions and asking me further questions before their class (which is the same class as I am teaching, just a different section). Maybe the instructor got jealous, I don't know.

The entrance to the classroom is from its front (not back), so I do stay in the front. But it is a big lecture hall, and there is a plenty of space in front of the room (the board itself consists of 8 huge panels).

Also, during my career as a grad.student who is also teaching for the department, I have had several observations from experienced professors who are considered to be great teachers at the department and are in charge of undergraduate teaching policy. In my evaluations the fact that there are always several students approaching me with questions after class considered as very positive, meaning that students find me approachable. 

Thank you everyone for answers. 
