Xamarin.iOS 8.6 issue with UIPickerViewModel overrides (and example workaround using UIPickerViewDelegate/DataSource). Reference material for Xamarin bug: https://bugzilla.xamarin.com/show_bug.cgi?id=25981.

ExampleViewController.cs

using System;
using UIKit;
using System.Collections.Generic;
using CoreGraphics;
using System.Linq;
using Foundation;

namespace PickerViewFailExample
{
	public class SomePickerViewModel : UIPickerViewModel {
		static readonly List<string> items = Enumerable.Range(1, 10).Select(i => "picker item " + i).ToList();
		public override nfloat GetRowHeight (UIPickerView pickerView, nint component)
		{
			Console.WriteLine ("GetRowHeight: {0}", component);
			return 50f;
		}
		public override nint GetComponentCount (UIPickerView pickerView)
		{
			Console.WriteLine ("GetComponentCount");
			return 1;
		}
		public override nint GetRowsInComponent (UIPickerView pickerView, nint component)
		{
			Console.WriteLine ("GetRowsInComponent");
			return items.Count;
		}
		public override string GetTitle (UIPickerView pickerView, nint row, nint component)
		{
			Console.WriteLine ("GetTitle: {0}:{1}", row, component);
			return items [(int)row];
		}
		public override NSAttributedString GetAttributedTitle (UIPickerView pickerView, nint row, nint component)
		{
			return new NSAttributedString (GetTitle (pickerView, row, component));
		}
		public override void Selected (UIPickerView pickerView, nint row, nint component)
		{
			Console.WriteLine ("Selected: {0}:{1}", row, component);
		}
	}
	public class PickerViewFailExampleViewController : UIViewController
	{
		UITextView SomeTextView { get; set; }
		UIPickerView SomePickerView { get; set; }
		public PickerViewFailExampleViewController()
		{
			SomePickerView = new UIPickerView () {
				DataSource = new SomePickerViewModel(),
			};
			SomeTextView = new UITextView () {
				InputView = SomePickerView,
				Text = "picker test",
			};
			View.Add (SomeTextView);
		}

		public override void ViewDidLoad ()
		{
			base.ViewDidLoad ();
			View.BackgroundColor = UIColor.LightGray;
			SomeTextView.Frame = new CGRect (new CGPoint (50f, 50f), new CGSize (View.Bounds.Width - 100f, 25f));
		}
	}
}

ExampleViewController2.cs

using System;
using UIKit;
using System.Collections.Generic;
using CoreGraphics;
using System.Linq;
using Foundation;

namespace PickerViewFailExample
{
	// This is a hacked-together workaround for UIPickerViewModel issues in PickerViewFailExampleViewController.
	
	public class SomePickerViewDelegate : UIPickerViewDelegate {
		public static readonly List<string> Items = Enumerable.Range(1, 10).Select(i => "picker item " + i).ToList();
		public override nfloat GetRowHeight (UIPickerView pickerView, nint component)
		{
			Console.WriteLine ("GetRowHeight: {0}", component);
			return 50f;
		}
		public override string GetTitle (UIPickerView pickerView, nint row, nint component)
		{
			Console.WriteLine ("GetTitle: {0}:{1}", row, component);
			return Items [(int)row];
		}
		public override NSAttributedString GetAttributedTitle (UIPickerView pickerView, nint row, nint component)
		{
			Console.WriteLine ("GetAttributedTitle: {0}:{1}", row, component);
			return new NSAttributedString (GetTitle (pickerView, row, component));
		}
		public override void Selected (UIPickerView pickerView, nint row, nint component)
		{
			Console.WriteLine ("Selected: {0}:{1}", row, component);
		}
	}
	public class SomePickerViewDataSource : UIPickerViewDataSource {
		int rowCount;
		public SomePickerViewDataSource(int rowCount) {
			this.rowCount = rowCount;
		}
		public override nint GetComponentCount (UIPickerView pickerView)
		{
			Console.WriteLine ("GetComponentCount");
			return 1;
		}
		public override nint GetRowsInComponent (UIPickerView pickerView, nint component)
		{
			Console.WriteLine ("GetRowsInComponent");
			return rowCount;
		}
	}
	public class PickerViewFailExampleViewController2 : UIViewController
	{
		UITextView SomeTextView { get; set; }
		UIPickerView SomePickerView { get; set; }
		public PickerViewFailExampleViewController2()
		{
			var pickerDelegate = new SomePickerViewDelegate ();
			var pickerDataSource = new SomePickerViewDataSource (SomePickerViewDelegate.Items.Count);
			SomePickerView = new UIPickerView () {
				Delegate = pickerDelegate,
				DataSource = pickerDataSource,
			};
			SomeTextView = new UITextView () {
				InputView = SomePickerView,
				Text = "picker test",
			};
			View.Add (SomeTextView);
		}

		public override void ViewDidLoad ()
		{
			base.ViewDidLoad ();
			View.BackgroundColor = UIColor.LightGray;
			SomeTextView.Frame = new CGRect (new CGPoint (50f, 50f), new CGSize (View.Bounds.Width - 100f, 25f));
		}
	}
}