I got the issue resolved. The issue was with the way, Topology Manager was mapping the Topology Settings in Discovery DB. I had two CD Servers, and each Discovery Service was mapped to respective Discovery DB. So, when I was running the Topology Manager Scripts, the Topology Settings was going into only one Discovery DB, not another. That is why we need to use only one Discovery DB for both Discovery Services and one Broker DB for Publishing, as Deployer URL is mapped in Deployer Capability in Discovery DB, and that can only be one.
But still one question though, what if we need to publish to file systems of Multiple Web Servers. However, I did a workaround to overcome this, as it is required in our Project.
We are now using two Discovery DBs for each Discovery Services. When Toplogy Manager settings is done, Discovery DB for Service 1 gets updated. Then we take backup of that DB, and restore in DB of Discovery Service 2. Once DB is restored for Discovery Service 2, we are running
java -jar discovery-registration.jar forceSync Command for Discovery Service 2. In this way, all Topology Manager Settings also go to Discovery DB, and the respective settings of Discovery Service 2 is also updated in DB. It resolved the issue in our project and now the sites are working absolutely fine on both servers.
Hope it helps.