You should have mentioned you were using the request library:
https://github.com/mikeal/request
request.post() is expecting the form either as the second parameter:
request.post('http://service.com/upload', {form:{key:'value'}})
or as a chained call:
request.post('http://service.com/upload').form({key:'value'})
Because you're not passing it as an argument, request.form() is not making any request at all, waiting for you to call .form(). But since you're not doing that either, no request ever happens, so no answer is ever returned, and thus your application sees that the request failed without response. You can see that in the chrome developer tools network tab, where the request will show a "(failed)" status code.
So just obtain the form data from the current request and pass it to request.form and it should work.
For future reference, a debugger would have told you what the mistake was instantly. I recommend the one included with Webstorm, but feel free to use any debugger at all.
Edit: Haven't tried but this is what I would try
app.post('/api.json', function (req, res) {
req.pipe(request.post("http://test-api.com/api.json", {form:req.body})).pipe(res);
});
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