Hello, thank you for reaching out to Microsoft Q&A.
May I please know if it is a Work or Personal Microsoft account?
Personal Microsoft account (e.g., ending in @outlook.com, @hotmail.com, @gmail.com that you created for services like Skype or Xbox) or a work/school account provided by an organization (e.g., ******@company.com)?
For a work or school account, there may be organization-level restrictions that might prevent access when signing in from another country or region. Like they block foreign logins or require VPN or additional verification for security reasons.
However, for a personal email account such as Outlook or Hotmail, you should normally be able to send and receive emails regardless of your physical location, as long as you have an internet connection and roaming or WiFi enabled.
Could you please confirm whether you experience the same issue when using Outlook.com in a web browser, rather than the Outlook iOS app?
Your incoming email should automatically sync with the Outlook servers and be available at Outlook.com in your browser. From there, you should be able to send and receive email as usual. So, instead of using your Mail or iOS Outlook app, you can use the Online version instead.
Meanwhile, sign in with your account on the additional security settings page here-
https://account.live.com/proofs/Manage
Note:
Ensure you have at least three verification methods, including an alternate email address to receive the verification code, active. Your phone may not receive the verification code when you are in another country.