This issue doesn't occur if you connect to Director server using Director FQDN.
Director server FQDN: director01.example.com
example: https://director01.example.com/Director

Issue only occurs using CNAME with underscore character
CNAME: r01_director01.example.com

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Remove the underscore character from the SAN certificate

 

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Problem Cause

CAUSE:
Security patch MS01-055 prevents servers with improper name syntax from setting cookies names. Domains that use cookies must use only alphanumeric characters ("-" or ".") in the domain name and the server name. Internet Explorer blocks cookies from a server if the server name contains other characters, such as an underscore character ("_").

Refer below article from Microsoft for more details:
https://support.microsoft.com/en-us/kb/316112 -PRB: Session Variables Do Not Persist Between Requests After You Install Internet Explorer Security Patch MS01-055

Citrix Director server logon fails with or without two-factor authentication using Windows Authentication method on IIS Error that we get is: "Cookies are not enable on the browser. Please enable and retry or contact your administrator"

https://ma.ttias.be/internet-explorer-wont-allow-cookies-subdomains-underscores/ -Why Internet Explorer Won’t Allow Cookies On (sub)domains With Underscores