I guess, UltraEdit is not capable in your environment to detect if an instance of UltraEdit is already running - see also
Multiple instances won't disable. UltraEdit must find itself in the Windows list of running applications. The full file name of uedit32.exe of one of the running applications must be identical with the full name of uedit32.exe called by the file manager (Windows Explorer).
I suggest to start UltraEdit first via the shortcut and then drag and drop the files to open into the main window of UltraEdit. What means drag and drop?
You mark several files in your file manager - Windows Explorer.
You click with the primary (left) mouse button on one of the marked files and hold the mouse button while you move the mouse pointer over the UltraEdit main window. If you can't see the UE main window, move the mouse pointer over the UltraEdit symbol in the Windows taskbar, wait there about 2 seconds and the UltraEdit window will appear, continue moving the mouse pointer and move it now over the UltraEdit main window.
Release the primary (left) mouse button when the mouse pointer is anywhere over the UltraEdit main window. UltraEdit will open now all the marked files.
With this method you have passed the full names of the marked files from your file manager to UltraEdit.