You're repeatedly prompted for your credentials in Internet Explorer when you try to access Microsoft SharePoint Online pages that contains embedded Sways.
The request window doesn't appear on other SharePoint Online site pages. After you enter your credentials, the window disappears. However, you're prompted again the next time that you access that page.
This issue occurs if Internet Explorer is crossing security zones between the SharePoint Online site (*.sharepoint.com) and the embedded Sway host site (*.sway.com).
To resolve this issue, add *.sway.com to the Trusted Sites zone. After you do this, the SharePoint Online site and "*.sway.com" are contained in the same Internet Explorer security zone.