>>...which is an extremely scaled down version of a real application

You're putting the candidate in a very vulnerable and stressful position:

You're potentially asking a candidate to solve a problem with your application (even if scaled down)--

The question/assignment could be a long-standing issue your staff have been unable to address on their own and you want to try to find out whether you can get a free solution from qualified people.

The candidate(s) could get the correct answer, yet you could walk away from the process with a free solution.

>> "I think very few people have ever declined"

That's short-sighted - they're not declining because the want/need a job and are already vulnerable during the process; many would not, understandably, have the presence of mind to decline.