Welcome to the Microsoft Q&A forum.
Based on the error received
Operation has exceeded maximum processing count. dnsResolverResourceId=/subscriptions/xxx/resourceGroups/xxx/dnsResolvers/xxx, circuitBreaker=[state=Open, processedCount=6, maxProcessedCount=5]
This issue can occur if the Microsoft.Network
namespace is not registered in your subscription. This requirement is mentioned here in the pre-requisites for Private DNS resolver.
If the Microsoft.Network namespace is already registered. Can you please try to re-register for it and see if it resolves the issue? (Please allow some time to pass before trying to deploy private DNS resolver again.)
Hope this helps! Please let me know if the issue still persists. Thank you!
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.