The information here is consistent with what I've learned.
You may have to purchase the application using your current Apple ID in order for it to work properly. Information/troubleshooting and there is a link to contact App Store support.
App Store Support
I can still "purchase" the app using my current Apple ID, but I can't because I no longer have access to my previous account information. App Store Support looks like a promising option.
Login using the old account credentials (if you remember them) if the password still escapes you go to iforgot.apple.com and reset it.
Alas, I don't have the old account credentials. Going to iforgot.apple.com looks promising, but I no longer have access to this information, and I've had no luck resetting this obsolete account.
You cannot transfer an app from one account to another.
But what you can do is recover your password for the other Apple ID. Here's how:
Changing your Apple ID passwordLearn how to change your Apple ID password.
Once you get all set up with the old Apple ID, you can log off the current one and onto the old one in the App Store and deal with (retrieve and manage) your app there.
I tried recovering the old password associated with the offending App, but no success so far.
With free apps, I could delete the old App and download a replacement. But with a paid App, the easiest way is to delete it, buy it again, and download it. This may be a job for the Apple Store.