Sometimes the download service seems to hang with an error such as “Reading the VMware software depot for the first time. This could take up to several minutes…”. One possible cause is an ongoing corruption issue with some of the underlying depot data files. This is documented in https://communities.vmware.com/thread/568541 and https://communities.vmware.com/thread/553547
In summary, the current issue relates to “corruption” in the dlg_ESXI60U3A.xhtml data file. Reference is made to a missing component (which seem ultimately to be files in the same directory).
The stdout-vapi_server.log file (stored in C:\Users\username\AppData\Roaming\VMware\Software Manager\Download Service) includes reference to the failing items, which can be removed one at a time. Once this is done (with the download service stopped) the service should resume working or report the next failing item. If the above error occurs, keep checking the stdout-vapi_server.log file for references to error items.