I finally came across this thread here,

http://gumstix.8.n6.nabble.com/LCD-touch-screen-unusable-on-Overo-Chestnut-td561488i20.html

Seems to be the same problem I'm having.

On Fri, Jan 13, 2012 at 2:48 PM, Stephen Farnsworth <robotoman@gmail.com> wrote:
I am having serious problems with the touchscreen on my 4.3" display.  I actually have two sets of Overo Waters + Chestnut43s and the problem is the same.

I set the environment correct, and occasionally the ts_calibrate program runs at boot.  I can usually get 1 touch event before it stops working completely.  Occasionally after trying holding the screen in many different positions and pressing with varied pressure, it registers a couple more touch events.  After awhile, it seems like I can get through the calibration, but the touchscreen continues to be unresponsive

The problem is consistent on 2 entirely different sets of hardware.

I've tried updating to the latest dev build of u-boot, and openembedded with no luck.  I've tried modprobe -r ads7846 && modprobe ads7846, etc...  Am I missing something or did I get a bad set of touchscreens?

-Stephen