What is a regular reboot and a hard reboot?
Do you mean powering the iPhone off and on, and an iPhone reset which is similar to a computer restart?
Have you tried this which was copied from Ralph's earlier post in this thread?
have you tried working through the iOS Troubleshooting WiFiguide? In most cases the culprit is not the iPhone unless something has actually failed, but a router that is not adhering to the IEEE 802.11 protocol strictly enough. If you choose to work through the troubleshooting tips, when you get to the part about shutting down the router you need to disconnect power to the router. Many routers do not shutdown when you hit the power button but instead go into standby mode. It has to be taken down all the way so it comes back up and gets a new IP starting address from the service provider.
If so with no change and you have forgotten your home network on the iPhone, have you also tried resetting network settings at Settings > General > Reset > Reset Network Settings?
If no change after that, is this a problem with your home wi-fi network only, or the same with every wi-fi network your iPhone has access to and connects with?
If with every wi-fi network your iPhone has access to and connects with, try restoring your iPhone with iTunes as a new iPhone or not from the iPhone's backup.