Power BI Report refresh based on condition- PBIRS

There is a possibility of a bit of work around.

Power BI Report Server creates a refresh schedule in SQL Server Agent job where it is hosted.

Now I think in your scenario you need to create 2 schedules for your report refresh. one that is scheduled other will be on-demand.

Once your stored procedure fails you can disable your current schedule 

EXEC msdb.dbo.sp_update_job Anonymous_name='JobName Scheduled',@enabled = 0

and then use this in your trigger in your log table whenever it updates or inserts new status to executes On Demand Job

EXEC dbo.sp_start_job N'JobName On Demand' 

to start your on-demand schedule and then enable your scheduled job when it finishes

EXEC msdb.dbo.sp_update_job Anonymous_name='JobName Scheduled',@enabled = 1