iPhone Mail App keeps asking for password.

I'm not sure if this is the right section, but here goes.

I have an iPhone 5S and my Mail App seems a bit temperamental.

More often than not, I'll open the App, and this will pop up:



I then type in the password, only for it to pop up with the exact same thing again, straight away. This usually happens for about 3-4 password entries, and then finally, it eventually logs me in and my inbox is refreshed/updated.

When it's actually logged in, I do get email notifications, but I am not getting emails, due to it "logging out" by itself all the time. To check my mail, I actually have to open the App up and go through the password hassle nearly every time. Very rarely does it stay logged in.

Any ideas as to how I can fix this and keep my Mail App logged in all the time?