icloud.com inbox not updating with new messages

My icloud.com mail inbox is not updating with new messages. I will see a new message arrive on my iphone but and it will not show up on icloud.com. I will then try to refresh/reload icloud.com. Sometimes this works right away but most of the time it takes 5 to 15 minutes and reloading the page 5 to 10 times before the message shows up on icloud.com. Sometimes icloud.com will just suddenly update and messages from an hour before will now appear. Also, even after a message appears, it will not let me respond to it or forward it right away. I have to wait for a while or reload it again before I can reply. Sometime I have to close the icloud.com tab and go to the page again to get it to work. It also will say I have X number new messages for a long period of time after I have already read the messages and/or deleted them.

I am using Internet Explorer 11. I do not have this problem with other mail programs (gmail, aol) on same web browser. How do I fix this? Is it something in my icloud settings with how mail is pushed or pulled?