Abhilash,

Think of the business case as an input to the project charter. Once the charter is complete, you do not need to worry about the business case anymore. Your project will need to meet objectives highlighted in the business case, but that's separate from the project management processes we learn in the PMBOK.

- Steven

The Business Case is not something monitored for closure.

The Business Case is an assessment and/or feasibility study which becomes an input to the Charter. It is used as a basis for a future project. In this regard, a Business Case is complete when it meets its goals. This study is then used with the Project, if that is the need, to support its justification.
The Business Case in a way is a self contained study, not something really closed, but something that could be used during a project.
I would also have to say that a Business Case itself, could be the result of a project meant to create one.

When do we consider that business case is closed. is it with completion of project charter or when we close the project.