We've got a Sony BRAVIA (not sure what model, top of my head) and have intermittent problems with both Wi-Fi and Ethernet connection.
Doing some searching around on forums and there seem to be similar problems but no obvious solution.
The only thing I've found which tends to work is to unplug the BRAVIA for about 10 seconds and then plug in and switch on, which usually resets it. Whether this causes the TV to reboot or causes the Internet connection to be reestablished, I can't tell, but it's the simplest, most reliable solution for now.
We tend to lose this connection maybe once per week - TV is used for several hours every day including significant Netflix/YouTube access.
Looking at the BT Hub connections, it still thinks the BRAVIA is connected throughout all of this. My gut feeling is the TV is at fault, as no other devices we have exhibit this behaviour.
Edit: Sorry, just noticed you said that Netflix still works but YouTube doesn't. That's odd, of course. We either have everything or nothing (unless the actual service itself is down, which is extremely rare.)
