My hotmail account as my MacBook Air mail consistently fails to login

I have my hotmail account as my MacBook email. However since I've been travelling through Europe it consistently fails to login. I've had this problem previously and had to verify my address with microsoft to ensure it is me trying to sign in in different locations. This morning, in Italy, it won't do it. I've successfully verified my email with microsoft, but Apple still won't allow me to access my mail through it's platform, consistently telling me that login has failed. Why, and how do I fix this? Thanks

[Re-Titled by Moderator]