You can practically eliminate the need to recharge EyeTV Mobile if you unplug it when you don’t need it.
If you leave the device plugged in while the app is not active, EyeTV Mobile cannot use the iPad’s battery and will therefore operate from the internal battery until it is drained.
If EyeTV Mobile’s battery does become fully drained, then connect EyeTV Mobile to a computer or USB power adapter to recharge it.
One example of an USB power adapter is what Apple provides to charge an iPod or iPhone via a power outlet.