The issue: 

Office 365 asks for log in creditials over and over again. (Even if you check the remember me log in box).

I have ran into this lots of times with different elements and different systems causing the issue so I am going to give you all the things that have worked for me.

Solution 1

Make sure your version of Office is up to date with all updates from Microsoft.

Start any Office 2013 or Office 2016 program.
On the File tab, click Account.
On the right side, click Update Options, and then select Enable Updates.
If you are asked whether you want to let Microsoft Office Click-to-Run make changes to your computer, click Yes.

Solution 2

Open an Office desktop app like Word.

Goto File> Options> Trust Center> Trust Center Settings > Protected View

Uncheck all the boxes and click OK

Solution 3 

Credential Manager (Search in start menu for it)

In the Windows Credentials tab
Click on the arrow near the "OneDrive cached credentials".
Check whether the OneDrive login credentials are listed over there.
If the credentials are listed, I suggest you to click on "Remove from vault and follow the onscreen suggestions.
Login to the OneDrive again and check whether the credentials are getting saved.

Solution 4 

When this error message comes up.
"Unsupported server The server you are trying to access is using an authentication protocol not supported by this version of Office"

Start an Office application that isn't OneDrive for Business. For example, start Word, Excel, or PowerPoint.
Click the File tab, click Account, and then click Switch account.
Click Add Account and then enter the Office 365 account that uses OneDrive for Business.
(Note Click SIGN OUT for any accounts other than the Office 365 account that uses OneDrive for Business.)
Exit the application that you opened in step 1.
Exit OneDrive for Business.

To do this, follow these steps:
Right-click the OneDrive for Business cloud icon on the taskbar.
Click Exit.

Start OneDrive for Business.
To do this, follow these steps:
Click Start, and then type OneDrive for Business.
Click the OneDrive for Business app.
Sync the OneDrive for Business library. To do this, follow these steps:
Right-click the OneDrive for Business cloud icon in the taskbar.
Click Sync now.