I just looked through the LiveView code and confirmed this issue happens when the LiveView code inside your iOS app can't see the LiveView server running on your computer. You claim that both your computer and your device are on the same network and the firewall is off. I suppose the next thing to check is the LiveView server even running?
LiveView lives inside the Appcelerator Studio directory. On my machine it's located at /Applications/Appcelerator_Studio/plugins/com.appcelerator.titanium.liveview.core_1.1.0.1445037865
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You can manually check the server status by running:
/Applications/Appcelerator_Studio/plugins/com.appcelerator.titanium.liveview.core_1.1.0.1445037865/node_modules/liveview/bin/liveview server status
There's actually a couple other subcommands you can pass in: start, stop, and restart. If the status command above says that the server is running, stop it using:
/Applications/Appcelerator_Studio/plugins/com.appcelerator.titanium.liveview.core_1.1.0.1445037865/node_modules/liveview/bin/liveview server stop
Build your app again and Studio will start the LiveView server again and hopefully this time it works. I don't think you need to manually start the LiveView server. I'm not even sure if that would work.
I hope that fixes your problem.