Phone will not stay connect to WIFI connections

When does it drop the signal? By design an iPhone will drop its Wi-Fi connection 30 seconds after the screen locks, to save energy, unless the phone is plugged in.

If it drops at other times, consider interference→Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support, especially if it only happens with your home Wi-Fi network and not with other networks.

Also make sure your home Wi-Fi router has the most up-to-date firmware available for it installed.