Why does iCloud.com log me out immediately?

Every time I try and login into iCloud.com using my correct user name and password. It opens for 1sec and logs back out. It will not stay open. I have my correct login info...but the site will not stay open for me to use it. I have tried on mu phone and a desk top...both with strong internet cellular data service and latest update. I've tried at work and at home. Why won't the website stay up?? I really need to get into it restore my calendar through "data recovery". Please help!!

[Re-Titled by Moderator]