I've read through this whole thread, as I was experiencing the same issue on my i6. The funny thing was that my wife's phone was not experiencing this at all, but I don't think its hardware related. We are both on 8.2, but the only difference is that I upgraded to iCloud Drive with my macbook air, and she has not.
I did manage to fix my phone for the past few hours- I can tell you now that none of the fixes in this thread worked.
This worked for me:
1. Turn off WiFi.
2. Hard reset the phone (home button + lock button for 5 seconds).
3. Turn phone on
4. Turn on WiFi.
So far my all networks are showing up, and its stable on my home network (WPA2 N router). The one caveat is that i do for an instant see LTE when I wake the iPhone, but not sure if that affecting anything.
I do think this is software related for sure, so don't waste your time going to an Apple store. v8.1 update will be released on Monday- wait until then and hopefully all issues will be resolved. (And we get Apple Pay! $$)
D