$request->send fails on one server but not the other
The problem was the service that was supposed to return the JSON feed was not returning anything. Meaning our server was simply waiting for a response that never arrived and eventually timing out a minute later.

I only discovered this by writing my own script to test for a response from two different servers, discovering the IP address of the server experiencing the problem was being blocked from accessing the JSON feed.

Please, if you're supplying data and decide to block someone's IP, at least tell them you're doing so. An error response would have saved me a lot of work.