I have/had the same problem with a T100TAM i just got. Everything was fine for a few days and then all of a sudden it started acting up yesterday. Working fine one startup, shutting it don, and then a hour later starting it up, without a working touchscreen. All i could find about the problem was this topic, so i did some more searching (instead of sending it back to Asus, which didn't work in your case).
I noticed that under device manager -> Human Interface Devices that there was a problem with the "I2C HID-Device". Some kind of hardware problem preventing the device from working and therefore disabled by Windows. After doing a repair installation of the Asus ATK Package and a reboot, it works fine again (problem is also gone in device manager) but after a few reboots the problem returns.
I think i traced it down to a optional Windows update i installed just before the problems started. The update is called: "Capella Microsystems - Light Sensor - Capella Micro CM3218x Ambient Light Sensor". I thought it couldn't do much harm but now i'm not so sure. After some research i found out that the Asus ATK Package a collection of drivers is, including those for the Touchscreen, Touchpad, Function keys and the Light Sensor. I have a hunch that the updated Light Sensor driver may have created a conflict in the ATK package causing a problem with the Touchscreen initialisation. I un-installed the Capella driver (in Device manager of Windows under Sensors, right click on the Capella light sensor and then select Uninstall), did one last Repair installation of the APK package, rebooted and thusfar no more problems. The optional update for the Capella light sensor is also back in the Windows Update screen, so i know for sure that it's not installed anymore.
Maybe the problems with return, but i've left it on, power save mode, rebooted it, turned it off and on and even left it off for an hour or so before turning it on. The problem hasn't come back. Hopefully it wont be back.
Perhaps this will help you, and other people who found this topic as well with the same problem. I'll keep this topic updated in case the problem comes back (or if it stays fixed).