I also have an HTC One X and had the same problem with my Wi-Fi. I've had the phone for about a month and every time I came home to my wireless network the connection would continuously drop on and off. I would watch it drop and obtain and IP in the Wireless settings.
I discovered the issue was my WPA Wireless network encryption was using AES, which seems to be an issue with this phone. I switched it to TKIP, and the issue was immediately resolved. My HTC Inspire, my previous phone, running Android 3.2 didn't have this issue, but my One X running Android 4.0 does. I'm assuming it is hardware, and not Android.