I can also confirm this same issue. Using either the standalone a2cmd.zip (from the link in this thread) or the EEK installer itself, it is not possible to run updates on any machine other than the one where the files were originally extracted. This has been an issue for quite a while.
I have tried this on a variety of windows 7 and 8 machines. Cannot vouch for vista or xp, though I somehow imagine the result will be similar. I probably first noticed this issue nearly 6 months ago when I first started using a2cmd. Has been around since then for sure, across any versions between that time and now.