That means bonjour is not working correctly for that machine. It happens sometimes. This is what you can try:
Go to the remote tab, check "Enable Access from Internet" and uncheck "Automatically Map Port".
In the iPhone client tap "+" to add server, chose "Enter Server Pin" and enter the server pin displayed on remote tab.
It's not reachable from internet because Air Video was told not to configure the server mapping. But if it's not reachable on local network that's bigger problem. It means something prevents Air Video Server for handling incomming connections. If you browse to http://localhost:45631 on the computer running Air Video Server, do you get any response?
If you get the Air Video response that means Air Video is running and the system firewall does not block it.
If you open safari on your iPhone and navigate to http://<your-computer-local-ip>:45631 do you get any response?
In this case it's most definitely problem with your network settings. Are both your iPhone and the computer even on same local network? What is the local IP address of the computer and the local IP address of iPhone? Maybe you have the network setup in a way that devices connected through WiFi are on different subnet than devices connected through ethernet?
Well, the computers really are on same local network. This is rather puzzling. As last resort you can try restarting both the router and the computer running Air Video Server but it's a long shot.
The bottom line is: if http://localhost:45631 gives you the response when you try it on the computer running Air Video Server
but when you connect to http://10.0.0.3:45631 from your iPhone and get timeout it means there are either routing problems or the firewall blocks it.
I'm sorry but I'm afraid I can't really help you with this - it's closely related to your network or windows configuration.