How can I “fix” damaged applications?

I recently attempted to open the App Store application iFlicks and received the following error message.

Unfortunately, this application has been removed from the App Store so I am unable to download it again. I have gone back through my Time Machine restoring different versions from different years but they all provide the same message.

My question, has anyone encountered this problem and, if so, how did you go about fixing the application? Further, how can this be fixed if the application has been removed from the App Store?