If you have successfully added the site to the Trusted Sites, you might still need to configure the O365 to keep you signed in.
Follow the Microsoft's documentation to do so:
If you previously didn’t check the Keep me signed in option and then browse to a SharePoint Online site or the Office 365 portal and you're already signed in, you must first sign out, and then sign in again by using the Keep me signed in check box. To do this, follow these steps:
a. In the Office 365 ribbon, click the drop-down arrow next to your user name.
b. Click Sign out.
c. Close all browser windows.
d. Browse to the Office 365 portal.
e. Select the Keep me signed in check box, enter your Office 365 work or school account credentials, and then click Sign in (if it’s necessary).
Open a document library in Explorer View.
- Try to access the mapped network drive.