New received mail problem

Hey everyone,

I got an iphone 6 a few days ago and yesterday I had a problem with my email.

I have a Microsoft Live account (example@live.com).

I received some new mail, but I cant see it in inbox. There is a notification I have one unread mail. On the bottom of the screen first the phone checks for mail, then it starts downloading it. For some reason, new mail is not downloaded.

First time this happened I tried turning my phone off/on and deleting and again setting up my account. It worked until today when I got the same problem. After quite some time I received the mail.

Could somebody please help me with this? What is the cause of this problem?

Also, is it possible to limit the number of shown mail in inbox?

Much appreciated!