Outlook continually asks me to sign in every time. How can I avoid this?

When you sign in to Outlook.live.com, look for the prompt asking "Stay signed in?" Select Yes or Do not show this again so the browser can retain your authentication session.

In addition, check your browser's cookie and privacy settings. In Safari, go to Safari > Settings > Privacy and make sure Block all cookies is unchecked. Avoid Private Browsing if you want your session to persist after closing the browser. Also, review any ad-blocking or privacy extensions, such as uBlock Origin or Privacy Badger, because they may interfere with Microsoft's authentication cookies. If necessary, add live.com and microsoftonline.com to the extensions' allowlists.

If the problem persists, clear the cookies and cached data specifically for live.com and outlook.com rather than deleting your entire browsing history. If you also use the Outlook desktop application or other Microsoft Office applications on your Mac, open Keychain Access using Command + Space, search for Microsoft, Outlook, or Exchange, and review any expired or duplicate authentication entries. Delete only entries you have identified as stale.

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hth

Marcin