Both scripts take about 10 seconds before failing. 10 seconds is the timeout for both connection and data transfer in the remote request.
To see which phase is failing, you could set one of the timeouts to 5 seconds. Set CURLOPT_CONNECTTIMEOUT to 5, for example, in both scripts.
It should be possible to figure out from the strace too.
Another good test would be to edit the script to make a remote request to example.com or google.com or something other than jetpack.wordpress.com.
Then, if the script still fails, it's clearly not the fault of jetpack.wordpress.com :) It must either be a problem with your host or the script itself.
Our servers respond to a lot of requests, so I don't think the resource limitation is on our end. It seems more likely that your host is limiting the resources available to any given user or process. Maybe an open file descriptors limit?
You can send the full strace to http://en.support.wordpress.com/contact/?jetpack=needs-service if you want me to look at it.
Mention me (mdawaffe) and let me know here if you do that so I can look at it promptly.