PBI Service not refreshing when using dynamic XLS sources

I have a dashboard connected to variety of dynamic data sources (XLS and XLSX from multiple websites). It refreshes fine in PBI Desktop but not in PBI Service.

I receive this error message when refreshing in PBI Service:

I have installed "AccessDatabaseEngine_X64" on my machine as both PBI Desktop and Office 365 are 64 bit but PBI Service still gives me the error message with every auto refresh attempt.

Have no problem with XLSX sources and it's only XLS sources are causing this issue in PBI Service. I know re-saving XLS sources in XLSX format will resolve this issue but XLS sources are coming dynamically from multiple web sources and I don't want making them static sources if re-saving in XLSX format.

Any thoughts or solution please?

Thank you.