private int taskID;
public override void DidEnterBackground (UIApplication application)
{
  if (this.taskID == 0)
  {
    this.taskID = application.BeginBackgroundTask(() => {
      application.EndBackgroundTask(this.taskID);
      this.taskID = 0;
    });
    ThreadPool.QueueUserWorkItem(delegate {
      for (int i = 0; i < 60; i++)
      {
        Console.WriteLine("Task {0} - Current time {1}", this.taskID, DateTime.Now);
        Thread.Sleep(1000);
      }
      application.EndBackgroundTask(this.taskID);
      this.taskID = 0;
    });
  }
}
public override void WillEnterForeground (UIApplication application)
{
  if (this.taskID != 0)
  {
 ...