Solution
In the NI-9237 Specifications you can see that the NI-9237 has a limited allowable common-mode voltage range relative to its excitation voltage (EX±). The NI-9237’s supported range is ±1 V around the excitation midpoint.

For example, for 10 V excitation, the NI-9237 supports a common-mode range of approximately 4 V to 6 V (midpoint = 5 V). At lower voltages, the NI-9237 input stage still has enough "internal headroom" to tolerate this offset. Once excitation rises past 8.5–9 V, the internal amplifier saturates, and the signal collapses.
You can check the sensor's common mode voltage range in the provided datasheet or measure the value using a DMM or a Scope.
Connect the sensor only to the external power supply, by powering the sensor with a 10V bench power supply (without connecting it to NI-9237), and use a DMM to measure the voltage across (AI-, EX-) pins.

With that data, you can determine the sensor's operating common mode voltage and verify whether the NI-9237 module can operate correctly with that common mode voltage or not.