Wowza streaming server causes "Failed Status Checks" on AWS EC2
I am running a low-latency audio stream application on a m3.large EC2 instance (Wowza Stream Engine 4.1.1 AMI). Whenever I open 100 or more tabs on my local computer's web browser, for testing reasons, connecting to the stream engine via RTMP, I get an Instance Status Checks failed on Amazon's Managements console. All connections abort and I can not even establish an SSH connection anymore.
Wowza's logs do not show any errors. And after rebooting, everything works again.