Cookie problem

This is not an expression engine problem, but I am absolutely stuck and wonder if anyone can shed any light on my problem. I have just moved to a new server and at first all was well. I am working on a ee custom system with lots of subdomains. On all but one subdomain it won’t save any cookies, so I get the login form, the message saying I’m logged in and back to the login form. The subdomain that works and the one that doesn’t has exactly the same code. Have restarted server and my computer and cleared out all the cookies to to be sure this is what is happening.

Does anyone have any idea what could possibly cause this problem?????