The way you are doing is not right.
Please use parameterized query.
Database
I have made use of the following table Hobbies with the schema as follows.

 
I have already inserted few records in the table

 
Note: You can download the database table SQL by clicking the download link below.
 
HTML
 
<b>Hobbies:</b>
<br />
<br />
<asp:ListBox ID="lstHobbies" runat="server" SelectionMode="Multiple">
</asp:ListBox>
<br />
<asp:Button ID="btnUpdate" runat="server" Text="Save" OnClick="Update" />
Namespaces 
using System.Data;
using System.Data.SqlClient;
using System.Configuration;
Code
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
        using (SqlConnection con = new SqlConnection(constr))
        {
            using (SqlCommand cmd = new SqlCommand("SELECT [HobbyId], [Description] FROM Hobbies"))
            {
                cmd.CommandType = CommandType.Text;
                cmd.Connection = con;
                con.Open();
                lstHobbies.DataSource = cmd.ExecuteReader();
                lstHobbies.DataTextField = "Description";
                lstHobbies.DataValueField = "HobbyId";
                lstHobbies.DataBind();
                con.Close();
            }
        }
    }
}
private void UpdateHobby(int hobbyId, bool isSelected)
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    string query = "UPDATE Hobbies SET IsSelected = @IsSelected WHERE HobbyId = @HobbyId";
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query, con))
        {
            cmd.Parameters.AddWithValue("@HobbyId", hobbyId);
            cmd.Parameters.AddWithValue("@IsSelected", isSelected);
            con.Open();
            int i = cmd.ExecuteNonQuery();
            con.Close();
        }
    }
}
protected void Update(object sender, EventArgs e)
{
    foreach (ListItem item in lstHobbies.Items)
    {
        this.UpdateHobby(int.Parse(item.Value), item.Selected);
    }
    ClientScript.RegisterClientScriptBlock(this.GetType(), "alert", "alert('Records successfuly updated!');", true);
}
Screenshot
 