The problem is your cookie domain. If you allow users to login to your site via both
http://www.yoursite.com and just yoursite.com., then you MUST have your cookie domain (AdminCP > Settings > Options > Cookies and HTTP Header Options > Cookie Domain) set to ".yoursite.com" (no quotes, but note the period at the beginning) or your users will have problems. Get that set correctly and the issue will be resolved.
(Your inline images are going to
www.site.com/attachment.php. The ones that are not inline just go to attachment.php. If you login at site.com, since your cookie domain is incorrect, you cannot see the images at
www.site.com.)