When you have put the phone to sleep it is supposed to disconnect from wi-fi when not in use. However, once you open it again, it should reconnect within a few seconds. You can go to Settings>General>Reset>Reset Network Settings. And just because there are no issues with other devices does not mean it is not the router. If after resetting network settings and then connecting to your wi-fi again, test. If you still experience a problem, then reset your router. Those steps are all contained in the support document I provided. If you still experience a problem, then create a current backup and restore your phone to that backup. One of these steps should correct your issue. If not, then make a Genius Bar appointment to have the device checked by Apple. Explain your issue to them clearly, and what steps you have taken to correct it.