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I think what you are saying is...
You have a default XOOPS installation... no hacks made to it.
You check the box to "save your cookie".
When you return to Xoops, it does not appear that a cookie was saved, because your username is not remembered.
Now some questions:
You looked through your cookies directory, and you don't see a cookie from your web site?
When you go to other XOOPS sites, and try to use this feature, it works?
When you try to access your site from other machines, it still doesn't work?
Are you using a domain forwarder? Or a system that puts a frame around your site to mask the domain? What can you tell us about your domain?
I note that I don't even see that feature at the xoops.org web site any longer. What version of XOOPS are you using?
There is this entry in the wiki:
http://wiki.xoops.org/wakka.php?wakka=XoopsAutoLoginHackHaving said all that, maybe don't bother with it, since both IE and Mozilla have a feature in the browser to remember passwords built-in. So if a user really needs that, they already have it.