I disagree — going down with the ship is stupid.
What you want to do is make it clear that the ship is heading for the rocks. Tell your employees as soon as you can see that there is trouble ahead, show them what you, and they, can do to avoid the rocks, and give them the opportunity to bail if they want to.
That way you’re not only avoiding the whole “boo-hoo, I’m the captain of the Titanic and nobody loves me” spiel, while giving yourself, and the people who depend on you, a chance to actually fix things before they go irrevocably to hell.
And that’s the important part, to be wise enough to see the rocks, to be honest enough to tell others that there are problems, and to be courageous enough to deal with them.