Several times I have seen that SQL Reporting services logs eat up disk space very rapidly. This usually happens on a SCCM primary server which also has been configured with Reporting Point.role. These logs usually don't provide any value so the easiest way is to disable them.
To disable SQL Reporting services logging navigate to \Program Files\Microsoft SQL Server\MSRS13.<instance name>\Reporting Services\ReportServer\bin, open ReportingServicesrService.exe.config file with Notepad, find DefaultTraceSwitch and set value to 0.
More information here https://technet.microsoft.com/en-us/library/ms156500.aspx
Update: In addition to previously mentioned, you also need to set correct this line in ReportingServicesrService.exe.config file:
<add name="Components" value="all:0" />