Interesting result. We do this all the time for a user community of ~5000 users without issue. The cookies from a citrix point of view will be different for each user session. Are you sure each user is not getting their own cookie? Maybe the browser on Citrix is not allowing cookies?
Are you sure that all users are coming from the same IP? Not sure how many users you have, but we load 20-35 users per server, and have 150+ Citrix servers running. Even if you use source address persistence, this will mean all users on a particular Citrix server will be load balanced to the same back-end server, but in our case, with 150+ Citrix servers, this is not an issue.
Talk to your Citrix admins and verify the config.
DeVon
Nimbostratus