My wife's iPhone 4s often switches away from our home wifi to 3g, even if she's just a few rooms away from the router. And once it's on 3g the web browsing is slow. Why doesn't her device stay connected to wifi? (And yes, I upgraded to Fios Quatum already, so the router would accommodate all the devices in our home.)
I would go into settings and turn off Cellular Data and see if you can stay connected to your home wifi.
you might like to post or review this situation at the Apple Support Forum http://www.apple.com
I would also check and see if your wifes iphone has updated to the latest OS which may have screwed up the phone.
As another remedy bring it to an Apple Store and let them look at it. Do not go to Verizon for it will not get fixed, they will want to get you a crappy junk refurbish phone. Don't trust that like new statement, and 100 point check etc. you may have worse problems with the replacement .