In the Classic Disney Shorts Donald's nephews were only staying with him until his brother-in-law got out of the hospital, after he was badly injured by a prank the triplets played on him. Since Huey, Dewey, and Louie never left, it implies their father died and the three are accidentally Self Made Orphans.
Actually, their mother left them there, but disappeared, along with the father, stranding them with Donald. And it was never spoken of again. The details depend on the author, though.
In Donald Duck comics, it is often mentioned that Donald is the sole guardian of Huey, Dewey, and Louie, which would imply that both their parents are dead.
Directly referenced in one of Don Rosa's comics, in which Uncle Scrooge mentions losing parents and one of the boys responds with "We know what that's like."
Speaking of the Don Rosa comics, if you consider the timeline canon and examine it carefully, you'll notice that Della had to have had the triplets when she was a teenager. That opens up all sorts of possibilities for why we haven't seen the father and why Della hasn't come back for her children.