Yes, it sounds strange. I purchased an app that didn't initially work and I requested a refund which was promptly processed by Apple. Then I couldn't find a better app for my needs and figured out some workarounds for the initial app. Now I still have the app installed on my phone and the honest thing to do is repurchase it. How can I do that?
It's not possible. Once an app is refunded, you cannot re-purchase it, for all eternity. I've spent about 2h with various levels of Apple support without success.
Also, it's worth mentioning that you cannot get updates for a refunded app (makes sense).