The situation is the following:

One of my players is a Hexblade warlock, pact of the Blade, however, his Hexblade is a dagger, and his pact weapon is a Rapier.

During a combat encounter, he threw his dagger at a retreating enemy, which lodged itself in his back, but managed to escape.

Did he just lose his hexblade? According to Hex Warrior, he can imbue any weapon with the might of his patron, does that mean that he can make any other weapon his hexblade?

Whats the ruling here?

It only lasts until you complete a long rest. The effect of turning a weapon into your hex weapon is not permanent - it's a temporary effect. When you complete a long rest you can choose one weapon to be your hex weapon and it remains so until you next complete a long rest.

The character also has 2 hex weapons since if you also have a pact of the blade then that pact weapon is also a hex weapon as well.

So, yes your character has lost his hex weapon (dagger) but still has his hex/pact weapon (rapier) and when he completes a long rest that dagger goes back to being a non-hex weapon, and he can choose a new weapon if he has one to be a new hex weapon.

Cool, that's just how i ruled it. Thanks for the advice.