Break the rules
This question arises from the already standard item system in most of the RPG games. The perfect example would be potions, there have been many memes regarding the collecting of potions, because "I might need them later".
Every RPG producer had to face the problem and many have failed. This comes from the wrong understanding that
"The item system works like this and it has to work like this, because every other game does it like this!".
But it doesn't. And The Witcher 3 proves it.
In The Witcher 3 the potion system works differently. Here you have a limit of potions you can carry, but after using them you can refill them anytime outside of battle using alcohol.
"But there will be no fun of searching for that legendary potion/item!"
You are right. After using your potion there will be no fun of searching for it again. However if not the system - the player wouldn't even use the item - meaning there would be no fun either. Players often prefer to die and fight again than to use that "too awesome to use" item.
This system brings a different "fun mechanic" though. Instead of searching for that potion you used in a fight, you will spend your time searching for an upgrade of that potion. It can even introduce additional quests to the gameplay.
In your case
There may be a thousand solutions to your problem and it's usually a bad idea to force a player to do something by external limits, like time limit or to reward player for using the item. Tynan Sylvester covers the topic in his book Designing Games: A Guide to Engineering Experiences. So before adding artificial rewards or punishments you should really consider advantages and disadvantages of that.
I already brought up the topic of potions in The Witcher 3, so to reflect it on your situation you could design the item to be "craftable". Let's say - you found that legendary weapon and will not use it in a fight, because you will lose it forever. But in our situation finding this item also allows you to craft it later. Or if the item was something magical - it allows you to summon it in a magic location.
It not only won't reduce the fun of using this item - it might increase it hugely by adding new mechanics to the game.
In any case you should still balance the item - "awesome" shouldn't mean "gamebreaking". If it is a single use item which kills a dragon in a second then it probably needs balancing anyway.