First of all... a point to be made about this Sword of yours.
If this is truly an "artifact" as you claim... and the damn thing breaks on every 20th swing... then that's a property of the item and not just "something that happens". Obviously, the point of the Sword's existance IS TO BREAK at various unopportune times, thereby making the wielder think it's worthless. If you follow the artifact creation rules, you'll see that if a character and the artifact grow further apart on their morals and beliefs, the artifact gets worse in terms of its abilities. So I would say that the reason the Sword Of Orcus breaks is because the wielder IS NOT the kind of person the artifact wants to be used by. Of course it doesn't want to be used by some goody-two-shoes adventurer! It is the weapon of the Demon Lord of Undeath. Its no wonder it allows itself to break in half when being used by your player (or all the other so-called adventuers who have found it over the preceeding centuries). If it truly breaks every 20th swing... then this has probably occured several hundred times over the course of it's existance.
Thus, everyone's ideas of the sword finding a new owner is a good one. That's probably what the Sword is looking for... an owner whose personality is more in sync with its own. When that occurs, perhaps the odds of it breaking grow less... so it's not on a Natural 1, but maybe two Natural 1s in a row. Or eventually as they grow more in sync, three Nat 1s. And if the owner and artifact are in complete agreement, there's no chance of breakage.
So based on the fact you created this Sword specifically to break on a 1 in 20 chance... you obviously did not intend for the party to have it for any length of time. So now that they realize that they had it but lost it... it's time to put it back into play by giving it to a new owner... someone who does what the artifact wants, and who the party now has to face in order to reclaim.
And forget the fact that you're afraid your party might think you a so-called "pushover". You're the DM. As they say in improvisation... you DON'T make mistakes, unless you actually admit that you did. As far as your players know... you fully intended for them to break the sword, think it's worthless, throw it away, and realize their mistake and want to back for it. It's only if you admit to them that you messed up your plot a bit by making the Sword not important enough for them to hold onto that they might start thinking they can keep getting away with stuff.
A DM doesn't make mistakes when it comes to plot, unless he actually announces it to his players. Anything that occurs in the story that the DM didn't expect, is now part of the story's canon... and it's your job as DM to pretend like you expected it the entire time and roll with what has occured.