Today I am seeing the same issue. Our 4 backup plans show a status "Running" with the last result for those jobs showing Success. No changes were made to these backup plans prior to this.
I hope someone has a solution.

Can you verify the version you are using, which backup storage you are using, the type of backup, and whether you are using the new backup format (released in 7.2) or the legacy backup format?

I also am seeing most of yesterdays backups as 'running' in monitoring, but they've completed with success status. Also never got the notification email about the job being completed.
All plans are legacy backup format, various agent versions from 6.3.5, 6.3.8, 7.2.0.

Can everyone confirm they are using the stand-alone CloudBerry Backup product and not our Managed Backup solution?

Our clients are 6.3.1.229 We use the mspbackups.com site to manage our server backups.

Our storage provider is Amazon S3 & Glacier.

The reason I was asking is this post is not in the managed backup section. It's in the standalone backup section which is why I needed to confirm. According to what I received from the team, this is a known issue because of a delay in processing by one of the server processes. However, it should right itself in a few hours. If you continue to see this status issue and lack of email notifications, please reply back here and I'll check back with the team.

I moved the post to the managed backup section.

Hi have open a support ticket here the answer:

Thank you for contacting the MSP360 Support Team.

It appears that issues with backup statuses on the web portal are caused by a degraded performance of one of the MBS web platform-related services.
The issue is now should be mitigated and no data is lost, however, in order for all the statuses to update and all new emails to be prepared several hours of propagation are necessary.

We have escalated your ticket to our Level 2 Support Team.
We'll get back to you as soon as we have any updates on this issue.

We appreciate your patience and understanding!

As far as I'm aware this issue only affects the status of backup jobs on the portal and email notifications. The backup plans themselves are not affected and should run with no issues.