Solution
This could be caused by the lead wire resistance. Quarter-bridge measurements are inherently sensitive to accuracy degradation due to the lead resistance of wiring from the sensor to the measurement device. The maximum usable lead wire resistance can vary, with a 120 ohm NI-9235 it's around 18 ohms but may vary between devices and resistances.
When using an NI 9235/9236 (the quarter-bridge modules), make sure the resistance of the strain gage you are using falls within the range listed in
What Resistance Ranges Can be Used with the NI 9235 and NI 9236?