Be sure and email support @ opto22.com and get those guys on the job.
My gut tells me, even though you have checked it, we are looking at a power supply issue.....
You measured 5.1 volts between the green terminal and the end of D2 (the diode nearest the capacitor)?
Also have you measured the RTD disconnected from the module? Pull the connector out the top and see if the problem persists.
Don't forget to measure for DC and AC (as well as resistance) on the probe in case there is a crossed wire or some amount of noise getting into the system.
Those are my quick thoughts on the matter.