Diehard fan / Die-hard fan
 

Someone who never gives up on his team. Win or lose he/she always roots for them. Never misses a game no matter what. What do you call someone like that in spanish?

Incondicional

"hincha a muerte (de X)" in Argentina

También en Chile.

Hincha a morir/hasta la muerte etc.

Tambien se usa en el Reino.

I found the adjective "diehard," one word rather than two, as empedernido. Does that help?

Perfect.

Not exactly for a fan:

un fumador empedernido ---> an inveterate smoker
un solterón empedernido ---> a confirmed bachelor
un criminal empedernido ---> a hardened criminal

Though die-hard could be sometimes rendered as empedernido, this term relates with rigidly repeating a behaviour, particularly one that is vicious. That's why we prefer other adjectives with positive uses of die-hard:

a die-hard romantic ---> un romántico incurable
a die-hard prankster --> un bromista incorregible