Before installing and starting Wowza, make sure you open the TCP ports 8087 and 8088 using Security Group setting, and you’ll have a smoother experience.
The long explanation: at the time I’m writing this, Wowza Streaming Engine works this way: it will attempt to use those ports, and should it fail to connect to a port (8087 I think), the engine manager will hang. At this time you may realise the issue and proceed to open the ports, but then you’ll have to manually unbind the ports (or reboot your EC2 instance – not just the wowza instance), so the engine manager can restart successfully. And yes, this is only a problem of the engine manager, the wowza media server instance itself still operates normally, as far as I’m aware.
This happens to me once, during my first time installing Wowza on EC2; I can’t be certain if it’ll happen to you in the same manner, but in case you run into a similar issue, hope this helps.
With all that said, it’s always been a pleasure using Wowza products.