Same problem with iPhone 5 since updating to iOS 7.1.1.
So far I have tried:
1) resetting network setting
2) restoring to factory settings to a new as well as to a backed-up setting
3) restarting wifi router.
4) using different wifi networks
What baffles me about this wifi problem is that despite pretty consistent and in apparantly unchanged signal strength, the actual measured speed/performance of the wifi has dropped significantly.
In order to ascertain what exactly is going on with the wifi, I ran a speed test on the wifi from different locations throughout my office. Near the router it still seems to work as well as before. Step a few feet away from the router and the wifi's speed seems to drop rapidly despite fairly consistent signal strenght (3 bars throughout). In actual numbers, my work's wifi used to have download speeds at about 11 to 13 kbps with a(n expected) neglible to moderate drop throughout the space away from the router. In earlier tests I had logged similar speeds throughout various locations in the office.
Presumably since the update to iOS 7.1.1, I am still able to measure 11 to 13 kbps in close proximity to the router, whereas about 25ft away (without any significant obstructions that may shield my reception), the wifi speeds drop to 0.5 to 1.0 kbps.
Surprisingly, my room mate who owns the same model iPhone and runs the same iOS version does not seem to experience these issues.
A visit to the apple store and a preliminary diagnostic test there only revealed that the wifi antenna itself seems to be fully operational.