When I hit the render viewport shading, it keep displaying the normal viewport. At the beginning of my project it worked perfectly but I stopped using the dual viewport, when I came to use it the second time, somehow it didn't work. Maybe I touched something I shouldn't?
I had the same problem a few days back. You must've accidentally set the render border too small to be visible hence it appears not to be rendering.
You can clear the render border by pressing CTRL+ALT+B or you can do it manually by going to the View>View Borders>Clear Render Border
You may have paused the viewport rendering. Check if the 'pause' button in the viewport menu/header is pressed.