foo.cs

static void Main(string[] args)
{
    var cts = new CancellationTokenSource();
    var token = cts.Token;
    var queryTask = QueryWebServiceInLoop("http://webapi/endpoint", token)
        .ContinueWith(t =>
        {
            if (t.Status == TaskStatus.Faulted)
                Console.WriteLine("faulted.");
        });
    Console.ReadLine();
    cts.Cancel();
    queryTask.GetAwaiter().GetResult();
}

static async Task QueryWebServiceInLoop(string url, CancellationToken cancellationToken = default(CancellationToken))
{
    using (var client = new HttpClient())
    {
        while (true)
        {
            cancellationToken.ThrowIfCancellationRequested();
            var response = await client.GetAsync(url,cancellationToken).ConfigureAwait(false);
            await Task.Delay(2000, cancellationToken).ConfigureAwait(false);
        }
    }
}