Hi Kunal,
Please ensure that before you drop te web part your page is checked out and after that you check in the page.
If the issue persists, create a web part page and try again.
During this process please bring up the Developer Tool (on IE hit F12 key), go to the tab Console and monitor for any js error.
Please let me know how it goes.
PS
I assume that you downloaded the shared version of qDiscussionView web part.
Ii you have the commercial version of the products then you got the qDiscussionView in that.
Also the shared (free) version is not compatible running on the same server with the commercial version.