The editor does not go to edit mode. The problem occurs also when Auto mode is used. This prevents the developers to rely on the AutoResizeHeight functionality when a mix of all rendering modes is required. 

Possible workaround is to use the RadDeviceDetectionFramework - http://docs.telerik.com/devtools/aspnet-ajax/controls/raddevicedetectionframework - and programmatically disable the AutoResizeHeight in mobile devices:

ASP.NET
<telerik:RadEditor ID="RadEditor1" runat="server" RenderMode="Auto"
    AutoResizeHeight="true">
    <Content>
        <p>editor</p>
    </Content>
</telerik:RadEditor>

C#
using Telerik.Web.Device.Detection;

public partial class Default : System.Web.UI.Page
{
    private void Page_Load()
    {
        if (Detector.GetScreenSize(Request.UserAgent) < DeviceScreenSize.Medium) {
            RadEditor1.AutoResizeHeight = false;
        }
    }
}