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Settings > General > Reset > Reset Network Settings
And then re-connect to the network you want.
NOTE: Doing this will make your phone forget every WiFi network it's remembered in the past and saved
Two things to try and fix. First, try doing a power cycle. Hold the power button down and the home button at the same time. Hold it for about 10 seconds until the phone turns off. Do not slide to turn off. Just wait. Reboot and try again.
If that doesn't work, it doesn't hurt to do a factory reset. Of course, back up your data either through iCloud or through iTunes. This way, you can find out for sure if it's the phones issue or just a glitch. Let me know if this works.