Node.js app begins timing out (ETIMEDOUT) when HTTP connecting to other sites after having been running for some time

I connect to other websites in my node.js app using the request module in a very standard manner:

Network.prototype.httpRequest = function(url, method, params, headers, callback)
{
    var qs = typeof params === 'string' ? params : querystring.stringify(params || {}),
        config = {
            'method': (method || 'get').toUpperCase(),
            'url': url,
            'timeout': this.app.api.settings.http.timeout_outbound
        };
    if(config.method === 'GET')
    {
        config.url += '?' + qs;
    }
    else
    {
        config.body = qs;
    }

    request(config, callback);
};

After a few hours of my app being alive, this function begins timing out -- and not just to one website. It begins to fail to connect (ETIMEDOUT) randomly, without any discernable pattern.

My first, obvious guess is that something must be somehow blocking/interfering with the network connections. There are plenty of other "moving parts" in my app (eg, connecting to Mongo via Mongoose, connecting to ElasticSearch via Elastical, etc.), so it is perhaps conceivable that one of them is the cause... but obviously, it's not really an option sit around selectively disabling other modules and waiting 6 hours to see if the problem goes away...

I'm monitoring network traffic (via iStatMenus pro on OSX, FWIW) and do not see any unusual / persistent traffic coming from node.

Is there any other way to delve into what might be blocking / interfering with my traffic?