In my opinion, Dr. Jekyll could not find a cure because he did not want to. You could argue that there was no need for a cure because there was not really any sickness that could not be overcome simply by Jekyll wanting to overcome it.
The potion that Jekyll devised could change him to Hyde or change him back to Jekyll. So getting back to being Jekyll was not a problem. The problem was that he did not want to stop being Hyde. You can see this from the fact that he once went two months without being Hyde, but then could not take it anymore.
So the cure was always there -- it was called willpower. But Jekyll didn't want to stop being Hyde, so no cure was possible.