Here are some ideas for you:
If you think the issue is static discharge, you can try using ESD control mats, ESD worksurfaces, operator ground straps, humidifiers, air ionizers and the like.
As page 3-5 of the AMUX-64T User Manual (http://www.ni.com/manuals) states
"The cold-junction compensation is accurate only if the temperature sensor
reading is close to the temperature of the screw terminals. Therefore, when
thermocouples are being read, you should keep the AMUX-64T away from
drafts or other temperature gradients such as those caused by heaters,
radiators, fans, very warm equipment, and so on."
Since you are making thermocouple measurements, that may be a factor. Also, thermocouples are not as rugged as other temperature devices and connections may not be
as secure.
I suggest stepping back to test without the thermocouples. Try grounding your inputs to read 0 V or using a battery across the differential inputs of a channel. Use the Measurement & Automation Explorer Test Panels for your DAQ board.
Regards,
Geneva L.
Applications Engineering
National Instruments
http://www.ni.com/ask