I have my Apple TV 2 jailbreaked with firmware version 4.4.4 (but had same problem on jailbreaked 4.3)
For some reason I can only ssh to the box when I plug in the network cable. When on wireless I can’t ssh (or even ping it). On wireless everything else seems to work fine, I have access to Netflix etc.
IP, netmask, router, and dns is the same on both wireless and wired. I have also tried to configure with a static IP address but that did not help either.