Symptom:
Your Backup and Sync enables you to log in, but in the next second you have been logged out.
(This error came after Windows 10 October 2018. upgrade.)
Solution:
Go to Task manager and stop the Backup and Sync process (GoogleDrivesync.exe).
Right-click it and select End process.
Type in %UserProfile%\AppData\Local\Google\ an Explorer window.
Locate any folder called "Drive" and rename it to Drive old
Reboot your machine or simply start Backup and Sync
Source:
Google Drive Help Forum
1.
Google Drive Help Forum
2.