So far I've found two ways to solve this:
1) The quick and dirty way (worked for me, but more a hack than a solution): Push your Web Dynos on Heroku to 2, connect JetPack, and then put the Dynos back to 1 or 0.
2) On the official Jetpack site: customize httpd.conf to allow for more concurrent connections:
http://jetpack.me/support/getting-started-with-jetpack/troubleshooting-tips/jetpack-heroku/
Hope that helps!