A mind as brilliant as Victor Von Doom's was always going to figure out a way to break the unbreakable, but in the case of Captain America's trusty shield, the Latverian dictator had to resort to dirty tactics.
The popular 1980s crossover event Secret Wars saw a god-like being called The Beyonder spirit the Marvel Universe's greatest heroes and villains away to a far-off galaxy to pit them against one another in the ultimate cosmic slugfest. One of those heroes happened to be Cap, and among the villains was Doctor Doom.
In issue #11, Doctor Doom stole The Beyonder's powers and the spotlight along with them. He used his abilities to lay waste to Cap and the other good guys, incinerating the lot of them with an energy beam. Among the ash pile that was once the Avengers, the broken remains of Steve Rogers's shield can be spotted.
This being Marvel Comics, all of the death and destruction is eventually reversed when The Beyonder tricks old metal face into resurrecting the heroes and reclaims his powers. He then grants each hero one wish, and Cap asks for his shield to be restored.