It may not be the phone. If the phone stays connected on other WiFis then I would say it is your home WiFi network.
Try forgetting the connection on the phone and reboot (turn off the power and then turn it back on) on the modem/router. Once it is fully powered back up, then try connecting with the phone again. If the problem continues, try turning off data on the phone. Sometimes the data and WiFi connects can conflict with each other.
Should it still not stay connected, then I would monitor your internet connection through a different device and see if your connection is dropping or fluctuating speeds a lot. If that is the case, the phone could just be sensitive to the issue, hence the dropping connection. If that is the case, then...