...but as you say, it makes no sense if the script does not run at all. Put some code both in your logon.bat, and in your KiX script that writes %COMPUTERNAME%, %LOGONSERVER%, and the date/time to a logfile.
Have you tried the GPOs for RunLogonScriptSync and/or for the Fast Logon Optimization? No clue why the MS forum would even suggest delaying the script until the desktop loads when many people do just the opposite with RunLogonScriptSync.
You really need to look into your AD design as I fell the problem lies there. Make sure the DNS SRV records are there and that DNS is working properly. Also make sure that each DC has a GC and that your sites are properly setup.
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Give a man a fish and he will be back for more. Slap him with a fish and he will go away forever.
