The key here is the desire, or preference, of the author. The author wants there to be a cure. He wants to be able to conclude that there is a cure, and so he does not want to conclude that there is no cure.
Unfortunately, after looking at the evidence, he finds that he is unable to do this: therefore, it is hard not to conclude that there is no cure. It's like saying "I am reluctantly forced to conclude that there is no cure", or, perhaps, "It looks like there is no cure. I have not formally made that decision yet, but it's hard to see how I can make any other decision"
Note that "Hard not to" isn't the same thing as "easy to" - the key difference is in what you might want to do.
Consider "It's easy to kill yourself with a gun" versus "It's hard not to kill yourself with a gun". The first is true - point it at your head and pull the trigger. The second is not true, because you can just put the gun down and walk away.