Please refer to the attached sample project and select a new value in the drop down.

Workaround: change the PageSize in the RadDropDownListElement.PopupClosed event:

public sealed class PageSizeDropdownHeaderCellElement : GridHeaderCellElement
{
    public PageSizeDropdownHeaderCellElement(GridViewColumn col, GridRowElement row) : base(col, row)
    {
        TextAlignment = ContentAlignment.TopCenter;
        Alignment = ContentAlignment.TopCenter;
    }

    private RadDropDownListElement _dropDownListElement;

    protected override void CreateChildElements()
    {
        base.CreateChildElements();
        _dropDownListElement = new RadDropDownListElement();
        if (_dropDownListElement != null && _dropDownListElement.DataSource == null)
        {
            _dropDownListElement = new RadDropDownListElement();
            _dropDownListElement.BindingContext = new BindingContext();
            _dropDownListElement.DropDownStyle = Telerik.WinControls.RadDropDownStyle.DropDownList;

            _dropDownListElement.Items.Clear();
            _dropDownListElement.Items.Add(new RadListDataItem("10", 10) { Selected = true });
            _dropDownListElement.Items.Add(new RadListDataItem("25", 25));
            _dropDownListElement.Items.Add(new RadListDataItem("50", 50));
            _dropDownListElement.Items.Add(new RadListDataItem("100", 100));
            _dropDownListElement.Items.Add(new RadListDataItem("All", -1));

            _dropDownListElement.Margin = new Padding(15, 0, 0, 0);
            _dropDownListElement.StretchHorizontally = true;
            _dropDownListElement.NotifyParentOnMouseInput = false;
            _dropDownListElement.Popup.MouseClick += Popup_MouseClick;
            _dropDownListElement.PopupClosed += _dropDownListElement_PopupClosed; 
            this.Children.Add(_dropDownListElement);
        }
    }

    RadListVisualItem elementUnderMouse;

    private void Popup_MouseClick(object sender, MouseEventArgs e)
    {
        elementUnderMouse = _dropDownListElement.Popup.ElementTree.GetElementAtPoint(e.Location) as RadListVisualItem;
    }
    
    private void _dropDownListElement_PopupClosed(object sender, RadPopupClosedEventArgs args)
    {
        if (elementUnderMouse == null)
        {
            return;
        }
        if (_dropDownListElement.SelectedIndex == -1)
            return;

        var pageSize = Convert.ToInt32(elementUnderMouse.Data.Value);
        if (pageSize == -1)
        {
            pageSize = GridControl.RowCount;
        }
        else
        {
            pageSize = pageSize <= GridControl.RowCount ? pageSize : GridControl.RowCount;
        }
        this.RowInfo.Tag = pageSize;
        GridControl.PageSize = pageSize;
        elementUnderMouse = null;
    }
    
    protected override void SetContentCore(object value)
    {
        if (_dropDownListElement != null && this.RowInfo.Tag != null)
        {
            this._dropDownListElement.SelectedValue = (int)this.RowInfo.Tag;
        }
    }

    public override bool IsCompatible(GridViewColumn data, object context)
    {
        return data is ActionColumn && context is GridTableHeaderRowElement;
    }

    protected override Type ThemeEffectiveType     
            { 
                get    
                { 
                    return typeof(GridHeaderCellElement);     
                }
            }
}