I had that problem when "Define" feature in Kobo app would not work on Ipad running on iOS 7.
To solve the problem, I had to use third party product - IBook, that is developed by Apple.
I opened any book in it, clicked "Define" and it also showed "No definition found" the same way as it was in Kobo app. However, on the bottom left corner, there was a "Manage" button, when I pressed on it, I was able to download Oxford Dictionary of English.
Afterwards, the issue with Kobo abb define issue has been solved.
I hope it helps!