TestPage.xaml

<?xml version="1.0" encoding="UTF-8"?>
<ContentPage xmlns="http://xamarin.com/schemas/2014/forms" xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml" x:Class="ListviewSelectTest.TestPage">
	<StackLayout x:Name="myStackLayout" Padding="0, 20, 0, 0">
		<Label Text="Clears selected when previous record is selected several times in a row (2-3 clicks)" BackgroundColor="Black" TextColor="#ADE9D5" />
		<ListView x:Name="ListClearOnOldRecord" HorizontalOptions="FillAndExpand" VerticalOptions="FillAndExpand" CachingStrategy="RecycleElement" ItemsSource="{Binding People}" ItemSelected="OnItemSelected_ClearOnOldRecord" ItemTapped="OnItemTapped_ClearOnOldRecord">
			<ListView.ItemTemplate>
				<DataTemplate>
					<ViewCell>
						<StackLayout x:Name="TemplateStack" Orientation="Horizontal" Spacing="10" HorizontalOptions="FillAndExpand" VerticalOptions="CenterAndExpand">
							<Label x:Name="FirstName" Text="{Binding FirstName}" />
							<Label x:Name="LastName" Text="{Binding LastName}" />
						</StackLayout>
					</ViewCell>
				</DataTemplate>
			</ListView.ItemTemplate>
		</ListView>
		<Label Text="Clears when any record is selected" BackgroundColor="Black" TextColor="#ADD8E6" />
		<ListView x:Name="ListClearOnEveryRecord" HorizontalOptions="FillAndExpand" VerticalOptions="FillAndExpand" CachingStrategy="RecycleElement" ItemsSource="{Binding People}" ItemSelected="OnItemSelected_ClearOnEveryRecord" ItemTapped="OnItemTapped_ClearOnEveryRecord">
			<ListView.ItemTemplate>
				<DataTemplate>
					<ViewCell>
						<StackLayout x:Name="TemplateStack" Orientation="Horizontal" Spacing="10" HorizontalOptions="FillAndExpand" VerticalOptions="CenterAndExpand">
							<Label x:Name="FirstName" Text="{Binding FirstName}" />
							<Label x:Name="LastName" Text="{Binding LastName}" />
						</StackLayout>
					</ViewCell>
				</DataTemplate>
			</ListView.ItemTemplate>
		</ListView>
	</StackLayout>
</ContentPage>

TestPage.xaml.cs

using Xamarin.Forms;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.Threading.Tasks;

namespace ListviewSelectTest
{
	public partial class TestPage : ContentPage
	{
		public ObservableCollection<Person> People { get; set; }

		private Person lastPerson;

		public TestPage ()
		{
			People = new ObservableCollection<Person> ();

			People.Add (
				new Person {
					FirstName = "Peter",
					LastName = "C",
				});
			People.Add (
				new Person {
					FirstName = "Tricia",
					LastName = "C",
				}
			);
			People.Add (
				new Person {
					FirstName = "Vicki",
					LastName = "Y",
				}
			);
			People.Add (
				new Person {
					FirstName = "Chris",
					LastName = "R",
				}
			);
			People.Add (
				new Person {
					FirstName = "Alan",
					LastName = "G",
				}
			);

			InitializeComponent ();
			myStackLayout.BindingContext = this;

		}



		protected void OnItemTapped_ClearOnOldRecord (object sender, ItemTappedEventArgs e)
		{
			Debug.WriteLine ("OnItemTapped_ClearOnOldRecord()");
		
			if (e.Item == lastPerson) {
				Debug.WriteLine ("Tapped Same Row - Try to Clear Selection");

				//	This appears to only work if you click several times
				ListClearOnOldRecord.SelectedItem = null;  

			} else if (e.Item != lastPerson) {
				Debug.WriteLine ("Tapped New Row");
				lastPerson = (Person)e.Item;
			
			}

		}



		protected void OnItemSelected_ClearOnOldRecord (object sender, SelectedItemChangedEventArgs e)
		{
			//if (e.SelectedItem == null) {
			//	Debug.WriteLine ("OnItemSelected_ClearOnOldRecord() :: e.SelectedItem == null (Called from Deselection)");
			//	return; //ItemSelected is called on deselection, which results in SelectedItem being set to null
			//} else {
			//	Debug.WriteLine ("OnItemSelected()");
			//}
		}






		protected void OnItemTapped_ClearOnEveryRecord (object sender, ItemTappedEventArgs e)
		{

			Debug.WriteLine ("OnItemTapped_ClearOnEveryRecord()");

			if (e.Item == lastPerson) {
				Debug.WriteLine ("Tapped Same Row");

			} else if (e.Item != lastPerson) {
				Debug.WriteLine ("Tapped New Row");
				lastPerson = (Person)e.Item;

			}

			// Setting SelectedItem = null here will deselect the listitem everytime, regardless of new record or not
			ListClearOnEveryRecord.SelectedItem = null; 

		}



		protected void OnItemSelected_ClearOnEveryRecord (object sender, SelectedItemChangedEventArgs e)
		{
			//if (e.SelectedItem == null) {
			//	Debug.WriteLine ("OnItemSelected_ClearOnEveryRecord() :: e.SelectedItem == null (Called from Deselection)");
			//	return; //ItemSelected is called on deselection, which results in SelectedItem being set to null
			//} else {
			//	Debug.WriteLine ("OnItemSelected()");
			//}
		}

	}

	public class Person
	{
		public string FirstName { get; set; }

		public string LastName { get; set; }

	}
}

Version Info.cs

Xamarin Forms - 2.0.1.6505

===============

=== Xamarin Studio ===

Version 5.10.2 (build 56)
Installation UUID: 3477b147-e3de-47d4-87f5-4f0230db8f1e
Runtime:
	Mono 4.2.2 (explicit/996df3c)
	GTK+ 2.24.23 (Raleigh theme)

	Package version: 402020030

=== Xamarin.Profiler ===

Version: 0.24.0.0
Location: /Applications/Xamarin Profiler.app/Contents/MacOS/Xamarin Profiler

=== Xamarin.Android ===

Version: 6.0.1.10 (Enterprise Edition)
Android SDK: /Users/matthewr/Library/Developer/Xamarin/android-sdk-macosx
	Supported Android versions:
		2.3   (API level 10)
		4.0.3 (API level 15)
		4.4   (API level 19)
		5.0   (API level 21)
		5.1   (API level 22)
		6.0   (API level 23)

SDK Tools Version: 24.4.1
SDK Platform Tools Version: 23.0.1
SDK Build Tools Version: 22.0.1

Java SDK: /usr
java version "1.7.0_71"
Java(TM) SE Runtime Environment (build 1.7.0_71-b14)
Java HotSpot(TM) 64-Bit Server VM (build 24.71-b01, mixed mode)

=== Xamarin Android Player ===

Version: 0.6.5
Location: /Applications/Xamarin Android Player.app

=== Xamarin Inspector ===

Version: 0.5.0.0
Hash: 45b35bb
Branch: master
Build date: Thu Jan 14 18:53:32 UTC 2016

=== Apple Developer Tools ===

Xcode 7.2.1 (9548.1)
Build 7C1002

=== Xamarin.iOS ===

Version: 9.4.1.25 (Enterprise Edition)
Hash: 962a050
Branch: master
Build date: 2016-01-29 16:59:11-0500

=== Xamarin.Mac ===

Version: 2.4.1.6 (Enterprise Edition)

=== Build Information ===

Release ID: 510020056
Git revision: bb74ff467c62ded42b7b7ac7fdd2edc60f8647b0
Build date: 2016-01-26 16:24:41-05
Xamarin addins: 8b797d7ba24d5abab226c2cf9fda77f666263f1b
Build lane: monodevelop-lion-cycle6-c6sr1

=== Operating System ===

Mac OS X 10.10.5
Darwin mMac.fios-router.home 14.5.0 Darwin Kernel Version 14.5.0
    Tue Sep  1 21:23:09 PDT 2015
    root:xnu-2782.50.1~1/RELEASE_X86_64 x86_64

Bug 38851 - [Forms] Unexpected Listview deselection behaviour (XAML)
https://bugzilla.xamarin.com/show_bug.cgi?id=38851