It is possible that there is a configuration issue with the registry entries related to the Analysis Services instances. The SQL Server Setup program uses the registry to identify the installed components and determine which components need to be updated or patched.
To troubleshoot this issue, you can try the following steps:
Check the registry entries related to the Analysis Services instances on the affected node and compare them with the registry entries on a working node. Make sure that the registry entries for all the Analysis Services instances are present and correctly configured.
Run the SQL Server Setup program in repair mode on the affected node and see if it detects the missing Analysis Services instances. If the repair mode does not detect the missing instances, you may need to manually remove and reinstall the instances.
If the above steps do not resolve the issue, you may need to contact Microsoft Support for further assistance. They can help you diagnose and resolve the issue.
It's also worth noting that patching a SQL Server cluster can be a complex process, and it's important to follow the recommended procedures and guidelines provided by Microsoft. Before patching a SQL Server cluster, it's a good idea to test the patching process in a non-production environment to ensure that everything works as expected.