They both sound correct to me. When I looked in "A Practical
English Grammar, 4th ed," (333), I found a similar construction:
"as" can mean "though/although" but only in the combination
ADJECTIVE + AS + SUBJECT + TO BE/ TO SEEM/ TO APPEAR
Tired as he was[,] he offered to marry her.
= Though he was tired[,] he offered to marry her.
Strong as he was, he couldn't lift it.
Even though your grammar does not follow the combination that they
described, I understood your sentences to mean the same thing:
Hard as he worked/As hard as he worked, he still went out of business.
= Though he worked hard, he went out of business.
Again, they both sound correct to me, but I would say that the "as ... as" construction is more common. And when I Googled "hard as he worked," most of the entries that seemed to mean "though/although" (in a similar construction) had "as" before "hard as he worked": for example,
As hard as he worked on the court and in the weight room, Clayton brought that same work ethic to his studies.
He worked hard to make a living, but as hard as he worked, he was always extremely active in the community.
As hard as he worked for Buster, Dick still wasn't making enough money to pay for college, and that was his ultimate goal.
As hard as he worked on playing baseball, he worked just as hard at learning English.
As hard as he worked to become an astronaut "” and as long as he yearned to do so, the reader gets the impression that Mullane had to regularly pinch himself and ask "what am I doing here?"
And as hard as he worked to make her sound Japanese, he worked just as hard to make Pinkerton sing like an American, in an American idiom.
As hard as he worked onstage "” where his band had to keep a close eye on his hand gestures, which indicated time changes, or risk being fined "” Brown was an equally harsh taskmaster in the recording studio.
But hard as he worked to improve as a sculptor and engraver, it was the order Durgin's received from a certain Dwight Davis for a silver trophy that would prove to be Rowland Rhodes's enduring masterpiece.
As hard as he worked, he played just as hard, Allen's friends and relatives said.
Hard as he worked, his income plummeted.
(This last one sounds somewhat similar to yours.)
I hope that this was helpful.