public class Consumer
{
    private readonly Service _service = new Service();

    public ReplaySubject<string> Results = new ReplaySubject<string>();

    public void Trigger()
    {
        Observable.Timer(TimeSpan.FromMilliseconds(100)).Subscribe(async _ => await RunAsync());
    }

    public Task RunAsync()
    {
        return _service.DoAsync();
    }
}

public class Service
{
    public async Task<string> DoAsync()
    {
        return await Task.Run(() => Do());
    }

    private static string Do()
    {
        Thread.Sleep(TimeSpan.FromMilliseconds(200));
        throw new ArgumentException("invalid!");
        return "foobar";
    }
}

[Test]
public async Task Test()
{
    var sut = new Consumer();
    sut.Trigger();
    var result = await sut.Results.FirstAsync();
}

public class Consumer
{
    private readonly Service _service = new Service();

    public IObservable<string> Trigger()
    {
        var connectible = Observable.Timer(TimeSpan.FromMilliseconds(100))
            .SelectMany(_ => RunAsync())
            .Replay();
        connectible.Connect();
        return connectible;
    }

    public Task<string> RunAsync()
    {
        return _service.DoAsync();
    }
}

[Test]
public async Task Test()
{
    var sut = new Consumer();
    var results = sut.Trigger();
    var result = await results.FirstAsync();
}

Observable.Timer(TimeSpan.FromMilliseconds(100))
    .SelectMany(async _ => await RunAsync())
    .Subscribe();