MainViewModel.cs

var canSearch = this.WhenAnyValue(vm => vm.SearchTerm)
    .Where(x => !string.IsNullOrWhiteSpace(x) && x.Length >= 3)
    .Publish()
    .RefCount();

SearchCmd = ReactiveCommand.CreateFromObservable<string, IEnumerable<string>>(term => Observable.StartAsync(_ => _movieService.GetMovies(term)).TakeUntil(canSearch));

SearchCmd.Subscribe(results =>
{
    Results.Clear();
    Results.AddRange(results);
});

canSearch
    .Throttle(TimeSpan.FromMilliseconds(500))
    .InvokeCommand(SearchCmd);