That's my story: I set at home about two days and used wi-fi permanently.
At one moment I noticed that phone with 3G, look at network - no routers around. I living at big home, so it's about 5 wi-fi access points possible to see.
After some switch on-off and reboot, I got 'grey wi-fi'.
Reset Networking settings helped out for a shortly time and it look likes
1 reset - no grey, 10 mintes of work - no avalible routers. Reset - no effect, one more, and one more.
Today at morning I reset my phone, restore with backup and got perma grey.
So, I made that trick with fridge.
15 minutes inside of freeze box, after that iPhone show me 'low battery, can't run', I start to charge it - suddenly it loaded and about 35% of charge, wifi started to work.
It still worked about 6 or 8 hrs.
But I think that should be hardware problem - wet or overheat.
Have no warranty (bought more than 1 year ago) and have no money for repair