Sounds more like a problem with your implementation. I'm pretty sure Puma can handle SSE just fine. Your implementation probably depends on EventMachine which is not baked in like it is with Thin.
content_type "text/event-stream" stream(:keep_open) { |out| settings.connections << out }
From Sinatra, which I assume is then deferring to EventMachine, courtesy of Thin. I'll see if there's a way of forcing EM directly in to the Stream setup...thanks for the pointer.
We recently wrote a demo demonstrating SSE on Phusion Passenger (https://github.com/phusion/passenger-ruby-server-side-events...). During writing of this demo, we found out that sinatra-contrib's streaming code relies on EventMachine. That means that sinatra-contrib's streaming only works on EventMachine-based servers, like Thin and on Goliath.
Based on my knowledge about Puma, I'm pretty sure SSE works fine on Puma as well. The Phusion Passenger SSE demo uses the Rack socket hijacking API (which we've blogged about: http://blog.phusion.nl/2013/01/23/the-new-rack-socket-hijack...) to implement SSE. This approach should work on Puma as well because it supports the Rack socket hijacking API too.