AHA!!
Now THAT makes sense. I suspect the problem is that your asp pages and aspx pages are running under two virtual application contexts. When cookies are written, they are being written with some path information that is causing certain instances of the cookies to not get sent back from the other page type.
If you are interested, you might try playing with the .Path attribute for the cookies. You could set this to "/" so that all cookies are relative to the server root and thus should be sent back regardless of which page type you are hitting.
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Peter