Proxied connection in Node Express app fails to close

Intro

I am using a Node Express app to proxy AJAX requests to a REST API because the API doesn't support CORS or JSONP yet. The Node app is running on Heroku. We have a reverse proxy setup in front of the Heroku app so that we can mount it anywhere we want in our domain (i.e., it's trivial to move from ourdomain.com/app to ourdomain.com/stuff/app).

The AJAX requests work great when I access the Heroku app directly. However, when I try to access the app through the reverse proxy, the AJAX requests fail with a connection timeout.

The Setup

The web client makes an AJAX request to the Heroku app via the reverse proxy

Web Client --> Reverse Proxy --> Heroku app

Then the requests get proxied to the API server which also sits behind our reverse proxy

Heroku app --> Reverse Proxy --> API Server

The requests don't fail if the app is accessed directly, thus skipping the reverse proxy the first time:

Web client --> Heroku app --> Reverse Proxy --> API Server

The Code

Here's an example of how I originally tried to proxy the requests. It fails when the AJAX request goes through the reverse proxy to the Heroku app but works if the app is accessed directly.

app.get('/proxy/*', function(req, res){
  var proxyURL = getProxyUrl(req);
  req.pipe(request.get(proxyURL)).pipe(res);
});

I was able fix the problem for GET requests with the following:

app.get('/proxy/*', function(req, res){
  var proxyURL = getProxyUrl(req);      
  request({
    url: proxyURL ,
    headers: {
      accept: req.headers.accept,
      authorization: req.headers.authorization
    }
  }).pipe(res);
});

I also need to proxy POST and PUT which aren't as easy. Here's what I tried for POST; it works when it doesn't handle requests that came through the reverse proxy.

app.post('/proxy/*', function(req, res){
  var rawBody = '';
  req.setEncoding('utf8');
  req.on('data', function(chunk) { 
    rawBody += chunk;
  });

  req.on('end', function(){
    var proxyURL = getProxyUrl(req);
    request.post({
      url: proxyURL,
      body: rawBody, 
      headers: { 
        'content-type': req.headers['content-type'],
        'authorization': req.headers.authorization
      } 
    }, function(e, r, body){
      res.send(body);
    });
  });
});

Notes

1. I have also tried node-http-proxy but that didn't resolve the issue.
2. We are using Node v0.8
3. Perhaps it has to do with Node not handling HTTPS proxies well, but I don't know enough about networking to understand the problem nor how it was fixed.