"Settings" hangs when scanning for WiFi since JB update on One X I have an HTC One X which has never before exhibited any connection problems. 

Since the update to Jelly Bean around 2 weeks ago, it cannot reconnect to a WiFi network once it has lost the connection. It stays on the 3G network by itself. When I go to Settings and select WiFi, Settings sometimes freezes still showing the normal Settings screen but not reacting to touches, sometimes the screen becomes black (the bar with the network information and battery level is still visible). I can still use the Home button to start other applications. At some point, I get a message telling me that Settings is not responding, prompting me to terminate it. 

When I restart the phone, it automatically establishes the connection to a known WiFi network. If I am somewhere where it doesn't find a known network, I can use Settings as usual to connect (scan for networks, choose one, enter password, connect). But after about an hour, I find that the phone is again on 3G and the above freezing happens when I try to reconnect. 

I think this is not a problem of the way the networks are set up, as I had the same symptoms in 4 different home networks, using different router brands. Many other devices, including other Android phones, function in these networks without a problem. 

A software update which came 2-3 days ago did not change anything about the problem. 

The phone is running Android 4.1.1, firmware version 3.14.401.31. It is not rooted. 

Any suggestions how to troubleshoot this? When I search the Internet for the HTC One X having WiFi problems, I only get scores of articles about known hardware problems.
I am using the same version of the OS on my HTC One X and I have never had this problem before. So I am thinking this is maybe a problem concerning the hardware of your phone. Maybe you should contact HTC for this problem. They can probably help you some more.

But you could always try to do a hard factory reset (this is something which HTC support will ask to do too) . Because an update doesn't really reset anything. A factory reset should reset all settings, this to make sure it isn't a problem of your settings. Before you do a factory reset, make sure you have a backup of everything.