Using MultiLine TextBox (TextArea) in EditItemTemplate of GridView in ASP.Net

Here I have created sample using your code.I have tested it in IE,Chrome,Forefox,etc.,you must check there may be css causing you this issue.

HTML

<div>
    <asp:GridView ID="gvData" runat="server" EditIndex="1" AutoGenerateColumns="false">
        <Columns>
            <asp:TemplateField SortExpression="Statement" HeaderText="Statement">
                <ItemTemplate>
                    <asp:Label runat="server" ID="lblStatement" Text='<%#Eval("Statement") %>'></asp:Label>
                </ItemTemplate>
                <EditItemTemplate>
                    <asp:TextBox runat="server" ID="txtStatement" Text='<%#Bind("Statement") %>' Rows="7"
                        TextMode="MultiLine"></asp:TextBox>
                    <asp:RequiredFieldValidator runat="server" ID="rfvedit" ValidationGroup="rfvg1" ControlToValidate="txtStatement"
                        SetFocusOnError="true" Text="Cannot be blank"></asp:RequiredFieldValidator>
                </EditItemTemplate>
            </asp:TemplateField>
        </Columns>
    </asp:GridView>
</div>

Code

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.Add("Statement", typeof(string));
        dt.Rows.Add("Statement1");
        dt.Rows.Add("Statement2");
        gvData.DataSource = dt;
        gvData.DataBind();
    }
}

Screenshot