Validity period of an open ssrs report
That's not how it works.

When you click a link in an existing report it basically opens the linked report with the parameters in the URL.

The target report has no clue about the rendering date of the source report.

If you want to accomplish anything like this you would have to pass the rendering datetime of the main report as a parameter to the subreport and have the subreport check that (every single one of them).

As far as I know there isn't a general setting and you would have to modify every drill-through action to send a parameter based on the datetime of rendering and modify each target report to check on it and render an error message if the parameter exceeds a certain threshold.