Development guide is missing description how to use Resteasy with Closeable apache httpclient.
The use case here is, that resteasy-client created with
Client client = ClientBuilder.newClient();

And this client throws TimeOutException, client is then not able to invoke any other requests to the server.
The solution can be to create own apache Closeable httpclient and pass it to ResteasyClientBuilder:

CloseableHttpClient httpClient = HttpClientBuilder.create()
                .setDefaultRequestConfig(reqConfig)
                .build();

Client client = ResteasyClientBuilder().httpEngine(new ApacheHttpClient4Engine(httpClient, true)).build();  // RESTEasy specific

This infomartion should be probably placed together within this chapter:
http://docs.jboss.org/resteasy/docs/3.0.9.Final/userguide/html_single/index.html#transport_layer