Have the exact same issue, and after spending over one hour at the Genius Bar I was told by the store manager that the only way to solve the issue was to buy a replacement phone because it wasn't IOS 7 to caused the issue but it was the wireless chip that was going to break regardless, and the iOS upgrade just accelerated the issue...
I have even showed her the plenty of threads like this one about the issue and she said they were all coincidences.
The thing is that the phone was brand new as it was replaced by apple 6 moths ago and super well taken care off...
I have been an iPhone user since the first hour and never had an issue till the 4s.
I'm super disappointed with the apple customer serviceman lack of care towards long time customers.
If you know your old phones won't work with the new iOS do not offer the upgrade.
It seems to me like a poor scheme to sell more new generation iPhones, since you can't even downgrade the iOS 6.
Now I'm stuck with a $600 clunker that can barely make phone calls since the 4g antenna is compromised, and that it's battery drains within 4 hours in plane mode wth no apps running.
I'm sad to say but it is time to get a windows phone or an android.
Shame on you apple...