How to reproduce: check the attached video

Workaround: create a custom MapSearchBarElement
public class MyRadMap : RadMap
{
    public override string ThemeClassName
    {
        get
        {
            return typeof(RadMap).FullName;
        }
    }
 
    protected override RadMapElement CreateMapElement()
    {
        return new MyRadMapElement();
    }
}
 
public class MyRadMapElement :  RadMapElement
{
    protected override Type ThemeEffectiveType
    {
        get
        {
            return typeof(RadMapElement);
        }
    }
 
    protected override MapSearchBarElement CreateSearchBarElement()
    {
 
        return new MyMapSearchBarElement(this);
    }
}
 
public class MyMapSearchBarElement : MapSearchBarElement
{
    public MyMapSearchBarElement(MyRadMapElement mapElement)
        : base(mapElement)
    { }
 
    protected override Type ThemeEffectiveType
    {
        get
        {
            return typeof(MapSearchBarElement);
        }
    }
 
    protected override void SearchProviderSearchError(object sender, SearchErrorEventArgs e)
    {
        IMapSearchProvider provider = sender as IMapSearchProvider;
        provider.SearchCompleted -= SearchProviderSearchCompleted;
        provider.SearchError -= SearchProviderSearchError;
 
        if (this.ElementTree != null)
        {
            UnsubscribeToTextBoxEvents(this.SearchTextBoxElement);
            RadMessageBox.SetThemeName(this.ElementTree.ThemeName);
            RadMessageBox.Show(e.Error.Message);
            SubscribeToTextBoxEvents(this.SearchTextBoxElement);
        }
    }
 
    protected override void SubscribeToTextBoxEvents(RadTextBoxElement textBox)
    {
        textBox.TextChanged += OnSearchTextBoxTextChanged;
        textBox.KeyDown += OnSearchTextBoxKeyDown;
    }
 
    protected override void UnsubscribeToTextBoxEvents(RadTextBoxElement textBox)
    {
        textBox.TextChanged -= OnSearchTextBoxTextChanged;
        textBox.KeyDown -= OnSearchTextBoxKeyDown;
    }
 
    private void OnSearchTextBoxKeyDown(object sender, System.Windows.Forms.KeyEventArgs e)
    {
        if (e.KeyCode == Keys.Enter)
        {
            this.Search(this.SearchTextBoxElement.Text);
        }
    }
}

1. Open the demo application >> Map >> Search example.
2. Enter some text and press Enter.
3. Move the mouse a little bit and you will notice the search box looses focus.

Workaround:  this.radMap1.MapElement.SearchBarElement.SearchTextBoxElement.TextBoxItem.LostFocus+=TextBoxItem_LostFocus;

        private void TextBoxItem_LostFocus(object sender, EventArgs e)
        {
            this.radMap1.MapElement.SearchBarElement.SearchTextBoxElement.TextBoxItem.TextBoxControl.Focus();
        }

In the scenario below one should be able to access the defined UserData value in the SearchCompleted event handler

How to reproduce:
protected override void OnLoad(EventArgs e)
        {
            base.OnLoad(e);

            this.radMap1.ShowSearchBar = true;
            BingRestMapProvider bingProvider = this.radMap1.Providers[0] as BingRestMapProvider;
            this.radMap1.MapElement.SearchBarElement.SearchProvider = bingProvider;

            this.radMap1.MapElement.SearchBarElement.SearchProvider.SearchCompleted += BingProvider_SearchCompleted;
        }

        private void BingProvider_SearchCompleted(object sender, SearchCompletedEventArgs e)
        {
            Telerik.WinControls.UI.Map.RectangleG allPoints = new Telerik.WinControls.UI.Map.RectangleG(double.MinValue, double.MaxValue, double.MaxValue, double.MinValue);
            this.radMap1.Layers["Pins"].Clear();
            foreach (Telerik.WinControls.UI.Map.Bing.Location location in e.Locations)
            {
                Telerik.WinControls.UI.Map.PointG point = new Telerik.WinControls.UI.Map.PointG(location.Point.Coordinates[0], location.Point.Coordinates[1]);
                MapPin pin = new MapPin(point);
                pin.Size = new System.Drawing.Size(20, 40);
                pin.BackColor = Color.Red;
                pin.ToolTipText = location.Address.FormattedAddress;
                this.radMap1.MapElement.Layers["Pins"].Add(pin);
                allPoints.North = Math.Max(allPoints.North, point.Latitude);
                allPoints.South = Math.Min(allPoints.South, point.Latitude);
                allPoints.West = Math.Min(allPoints.West, point.Longitude);
                allPoints.East = Math.Max(allPoints.East, point.Longitude);
            }
            if (e.Locations.Length > 0)
            {
                if (e.Locations.Length == 1)
                {
                    this.radMap1.BringIntoView(new Telerik.WinControls.UI.Map.PointG(e.Locations[0].Point.Coordinates[0], e.Locations[0].Point.Coordinates[1]));
                }
                else
                {
                    this.radMap1.MapElement.BringIntoView(allPoints);
                    this.radMap1.Zoom(this.radMap1.MapElement.ZoomLevel - 1);
                }
            }
            else
            {
                RadMessageBox.Show("No result found for the provided search query!");
            }
        }

        Telerik.WinControls.UI.Map.Bing.SearchRequest request;
        private void radButton1_Click(object sender, EventArgs e)
        {
            Telerik.WinControls.UI.MapLayer pinsLayer = new MapLayer("Pins");
            this.radMap1.Layers.Add(pinsLayer);

            request = new SearchRequest();
            request.Query = "San Marino";
            request.SearchOptions.Count = 10;
            request.SearchOptions.QueryParse = true;
            request.UserData = "Tooltip";
            BingRestMapProvider bingProvider = this.radMap1.Providers[0] as BingRestMapProvider;
            bingProvider.SearchAsync(request);
        }

Workaround:  if possible cache the data to be accessed at a later stage