Zach,
The instrument probably does not drift linearly forever or the value would eventually go out of range. The manual I donwloaded requires 30 miniute, 4 hours, or 24 hours of warmup time, depending on the model and the application.
Can you try to record the readings once per minute for 24 hours starting with a cold intstrument and letting it run in as stable an environment as you have available? Record the ambient temperature also, if possible. Does the drift ever stabilize?
How large is the drift compared to the signal you need to measure? How fast is the drift? How fast does your fluid dispensing change the readings?
Lynn