iPhone SE not showing WiFi icon on screen

Under Settings > WiFi, my iPhone shows that I am connected to a network. When I connect to this network, the WiFi icon pops up for a split second at the top of my screen, and then it disappears. And so there is no WiFi icon after that, and the phone cannot connect to the network. I have tried restarting the phone, forgetting the network, and resetting network settings. None of those things worked. Any suggestions?