Remote Buddy saves the result of the verification using the OS X preferences system. If that system does not work correctly - f.ex. due to file system permissions or zero length files - you'll see the effect you observed.

Depending on whether you chose to save the license for all users or just the current user (default), OS X may have created files in different locations to match all (/Library/Preferences/[ByHost]/) or just the current user (~/Library/Preferences/[ByHost]/). If you run

ls -al /Library/Preferences/com.iospirit.*license* /Library/Preferences/ByHost/com.iospirit.*license* ~/Library/Preferences/com.iospirit.*license* ~/Library/Preferences/ByHost/com.iospirit.*license*

in Terminal.app, you'll see where OS X stored the com.iospirit.RemoteBuddy.license.plist file(s) on your Mac. Next steps:

1) Quit Remote Buddy 
2) Delete (or move elsewhere) the license preference files found above. 
3) Make sure OS X preferences doesn't still have a cached copy of our preferences files by entering the following into Terminal.app

killall cfprefsd

4) Launch Remote Buddy and go through the verification. Be sure to NOT tick the "all users" option, as this seems to be where OS X Yosemite fails to perform correctly for some.

Hope that helps!

Cheers, 
Felix