I don't know, Jim... I have the same problem with wifi persistence in iOS6, and I'm using an Apple Airport Express with all the current firmware. It would seem to me, that if it is a router problem, it wouldn't be happening with their own routers...
What's the next "excuse"?
I do have to say I think you are partially right on one issue.
I've read most of the pages on here, and maybe someone has already brought this up, and I missed it, but you are right in saying that previous iOS's did shut off wifi when the phone went to sleep (and not plugged in)... but what you're not understanding is the exceptions to that. As far as I understand, with previous iOS's, if the phone had access to cellular data and it went to sleep, wifi would be disconnected. If a push notification came through, a cellular packet would be sent to the phone to wake it and have it connect to wifi. That way, even with the phone sleeping (and not plugged in) you would be able to get iMessages, Skype calls, etc.
In previous iOS's, if the phone did NOT have access to cellular data and went to sleep, wifi would stay on to get all the pushes.
iOS 6 changed this and now wifi shuts down upon sleeping regardless of whether or not the phone has access to cell data.
You can do all the ping tests you want, but I'll tell you that iPhones with iOS6 behave differently than ones with previous iOS's.
The proof is in the pudding... I'm an airline pilot and I spend half the month at international locations. I have an iPhone 4 (and I've had it for a long time, so I know how it acted), and before I get to my international layover, I activate call forwarding to send my cell calls to my Skype In phone number, I turn ON Airplane mode, then turn wifi ON. When I get to the hotel, I set up my Airport Express in my room, so I can have a hotspot.
Prior to iOS6, my phone could be unplugged, asleep, and locked, anywhere in my room and if someone called my cell, my Skype would ring. If someone sent me an iMessage, I would get notified. If I got an e-mail, my phone would "ding." I could sit at a coffee shop in Shanghai or a cafe in Paris, hooked up to their wifi... phone asleep on the table and if my wife called me, Skype would ring through.
Now, with iOS6 it DOES NOT WORK THAT WAY. I do not get Skype calls, I do not get iMessages, I do not get e-mail notifications, my family can not FaceTime me, if I am not tethered to the wall with a power cord. It does not work the way it did with iOS5. Period. This iPhone was my lifeline to my family when I was half way around the world for years, I know how it worked. It's different now. You can tell me until you are blue in the face that nothing changed, but you are wrong. You can ping away at your phones, but iOS6 is broken, making the phone about useless for me, and probably tens of thousands of others who travel frequently or just don't have constant access to cell data in their day-to-day lives.