Hi,
Thanks for posting on our forum!
Based on your descriptions, it seems that when enabling your third-party backup tool, your network occasionally lose packets. When you disable the tool, this issue disappears, so I guess this third-party tool may take up a lot of bandwidth when it is in the run. In this case, you can:
1) Add an extra network cable
2) Increase cluster heart rate threshold. See:
https://www.virtual-dba.com/blog/always-on-changing-cluster-configuration/
Please note: Information posted in the given link is hosted by a third party. Microsoft does not guarantee the accuracy and effectiveness of information.
In addition, you can also check other causes and solutions for this issue through this article:
https://learn.microsoft.com/en-us/windows-server/troubleshoot/troubleshooting-cluster-event-id-1135
Thanks for your support!
BR,
Joan
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