The detection of an already running instance works only if the application is started with the same path. That's the reason why I asked for a second uedit32.exe.
I think on your computer there are different paths to uedit32.exe. Look at all shortcuts (*.lnk) which contain uedit32.exe if they all have the same and correct long path to uedit32.exe. Start Regedit and search also for all occurrences of uedit32.exe and check the paths. They should be all identical and should be all correct. Check also the environment variable Path if it contains the path to uedit32.exe and if so, if it is also correct and only once present.
Have you upgraded your current installation from a previous one? The default installation directory has changed in the past and so it's possible that in the registry different paths to uedit32.exe exist, but the EXE is found automatically by Windows via the Path variable or the uedit32.exe key in "HKLM\Software\Microsoft\Windows\Current Version\App Paths" or other caches in the registry.
Search in the whole registry also for ue32ctmn.dll and check the path to it. It must be the same as to uedit32.exe.
My last advice is to use Filemon and Regmon from Sysinternals
to detect what's going wrong on your computer.