Please, specify if you can sign in and add files to OneDrive.
If the answer is yes - please send logs to our support for further investigation.

Just an update in case anyone else encounter the same issue:
It is related to API limitations on Onedrive side. Uploads are being throttled due to the amount of data transferred.

What did you have to do to fix this issue?

What kind of files do you fail to upload? The main thing is to consider permissions for the account - check out: https://support.office.com/en-us/article/Permissions-needed-to-upload-files-in-OneDrive-for-Business-c0d770b2-5165-403d-9d58-62946bcf46dd

Since that is API limitation on MS side we currently can suggest modifying certain configuration parameters manually, that can help.

1)
- close the Backup application
- open settings folder: C:\ProgramData\CloudBerryLab\CloudBerry Backup\
- find file enginesettings.list
- edit this file with notepad
- Find the string "10000000"
- change 10000000 to 2000000
- close and save the file
- restart the Backup application

2) Reduce number of threads (Tools/Options/Advanced) to 1.