I have added the particular workstation once and then deleted it, now I can't add it again.
I can see the workstation is there when I just search for it, but whenver trying to add it through "membership rules", it's not appearing there so, I can't add it.
The effective way to add them in SCCM is to configure SCCM discovery methods.
This blog article will explain the various discovery methods and will describe how to configure it.
In this post we will be seeing the steps to install configuration manager clients by using client push method.
Microsoft suggests to use the client push installation to install the System Center 2012 Configuration Manager client software on computers that Configuration Manager discovered.
Applies To Software Update Cycle is captured as an ' Event' for Patch Management.
Before you start thinking of deploying the configuration manager clients, install a fallback status point site system role.
The benefit of installing this role is it helps to track the client installation process.
Here’s the official discovery methods definition from Technet : SCCM discovery methods identifies computer and user resources that you can manage by using Configuration Manager.
It can also discover the network infrastructure in your environment.
Can you try updating the collection membership manually or refresh so the computer might appear again after discovery cycle?