Why can't I measure resistance when there is current on the potentiometer?
Because your multimeter can't measure resistance. So it applies a known current, measures the resulting voltage, and computes the resistance from that. 1

So when you're applying an external current to the potentiometer you are upsetting the meter's procedure, and the resulting voltage is probably outside the measurement range.



1 Unless it's really old. In which case it applies a fixed voltage, measures the current, and lets you read the resistance off an inverse scale.