Request password for every report

More appropriate solution would be to delete all the reports and redeploy all the reports. Steps are as follows:

First step is to delete all the existing SSRS Reports. For doing this you can navigate to DynamicsAx folder and delete the entire folder.

Then go to Report servers form in Dynamics Ax 2012 Tools > BI > Report server and click on "create report folder" button to create the Folder DynamicsAx again.

Now you can open Powershell (Administrative Tools > Microsoft Dynamics Ax 2012 Management Shell). Make sure you run Powershell as Administrator.

Deploy all the reports with the help of command:

Publish-AXReport -ReportName *

And once, all the reports are deployed you should be good to go.