Hello Alexandra,
It is not annoyed as you think. It is a protection. But if you don't want hotmail to keeps asking you, try this below
If you use Edge Browser>click 4 dots (....) on right top of your Browser>settings>scroll down>Passwords> from there
click on +Add > it will ask
webURL : outlook.com or Hotmail.com
Username: yourEmailAddress
Password: yourEmailAddress password
In category select email
Add note optional
Click on save button to save them and close al your browser and start it again. Now it shouldn't ask you again and again. try it. Don't clean your history otherwise you will loose it. And tell me if that works for you.