In Windows 2003 Server, one can not enable offline files when Remote desktop is enabled on the machine. If you do not see anything in offline files tab (like above) in Folder options windows then check if Remote desktop is enabled on the machine.
In Windows XP, one can not enable offline files when Fast user switching is enabled on the machine. If you do not see offline files tab in Folder options then check if Fast user switching is enabled on the machine.
Sometimes users see “enable offline files” option greyed out in the Offline Files tab. This happens when the group policy is set to disable offline files. This locks the offline files UI and users will not be able to change any setting. You might have to contact the administrator at your workplace to get the the group policy modified to enable offline files.