How do I prevent an app from adding itself to the list of Login Items every time it starts?
The app in question is Unified Remote, which seems to completely wonderful apart from this "bug".
Your best option is to contact the developers of Unifed Remote directly. This way they will know it is a problem and may be able to offer an immediate solution.
Otherwise, you might want to investigate scripting the removal or quitting of the Login Item. The Mac Stuff web site has a good overview at Adding and deleting login items using AppleScript:
tell application "System Events" --Find out what login items we have get the name of every login item --see if the item we want exists. If so then delete it if login item "home" exists then delete login item "home" else display dialog "That login item doesn't exist" end if end tell