Vikash,
I would not recommend you to use this model for your website.
You need the connection open only for a particular database operation(s), after that you have to close the connection, otherwise you are doomed to some memory consumption problems and database lock issues.
Instead, I would recommend you the following construct:
1. create/open connection
2. do some operations against the database
3. close the connection immediately after.
In c# there is a pattern for doing such things:
using (SqlConnection con= new SqlConnection("connection string"))
{
con.Open();
}
Good luck.