How to keep single SQL Server connection instance open for multiple request in C#?

I have a Web API which contains database insert logic (ado.net) in C#. When multiple users (e.g. 100 users) call the Web API, every time a SQL Server connection is opened and closed for multiple requests. It slows down performance.

How can I keep a single SQL Server connection live for multiple requests? I have to keep SQL connection open only once and close after some time so that during that time it should consider multiple request and insert records in database.

Please suggest.

ADO.NET's SqlConnection is implementing a connection pool. This means that when you close or dispose an instance of SqlConnection, the underlying connection simply returns to the pool. When another instance of SqlConnection is opened, and a connection is available in the connection pool, that connection will be used.
In fact, Microsoft docs page on SQL Server Connection Pooling clearly states:

Caution
We strongly recommend that you always close the connection when you are finished using it so that the connection will be returned to the pool. You can do this using either the Close or Dispose methods of the Connection object, or by opening all connections inside a using statement in C#, or a Using statement in Visual Basic. Connections that are not explicitly closed might not be added or returned to the pool. For more information, see using Statement or How to: Dispose of a System Resource for Visual Basic.

This means that the best practice way of using SqlConnection is this:

using(var con = new SqlConnection(connectionString))
{
    // your sql stuff goes here...
}

BTW, SqlCommand, SqlDataReader and SqlDataAdapter also implements the IDisposable interface, so they too needs to be used in the context of the using statement:

using(var con = new SqlConnection(connectionString))
{
    using(var cmd = new SqlCommand(sql, con))
    {
        // prepare command here - parameters and stuff like that

        // either
        using(var reader = cmd.ExecuteReader())
        {

        }

        // or 
        using(var adapter = new SqlDataAdapter(cmd))
        {

        }

    }
}