first-party cookies are the Mendix cookies, assuming you access the mendix application directly.
is InPrivate Browsing enabled perhaps?
Hello,
See this.
https://serverfault.com/questions/161221/cannot-get-iis7-to-send-cookies-to-ie
It seems the IIS doesnt treat the URLs well if the host name has '_' in them. It is an indicator for it to send
Does your URL has a '_' in the host name? is it an option to change the URL?