We had a similar problem, caused by the <add key="CMSSharedFileSystem" value="true" />
in the web.config
. If set to true, Kentico assumes that the local search indexes are on shared storage. It disables the generation of web farm tasks related to synchronization of physical files (media library items, smart search indexes, etc.). See Configuring web farm servers - Web farm instances with a shared file system.
If your storage provider is not configured correctly, the indexes will stay local, there will be no synchronization and no errors in the logging. In your storage initialization module, you have to do something like this:
const string AzureSmartSearchStoragePath = "~/App_Data/CMSModules/SmartSearch";
AbstractStorageProvider smartSearchProvider = StorageProvider.CreateAzureStorageProvider();
smartSearchProvider.PublicExternalFolderObject = true;
StorageHelper.MapStoragePath(AzureSmartSearchStoragePath, smartSearchProvider);