I've never seen measurements that erratic. I always look at the measurements to make sure nothing looks wrong after calibrating, so I've probably seen that screen several hundred times.
The Fiery forum thread referenced by ColorMonkey seems to talk mostly about profile issues, but since the wacky curves are the measurements (rather than the target), I wouldn't think the profile would be to blame.
My guess is something is wrong with the spectrophotometer, or the Fiery's interpretation of its data. The actual raw readings are usually much more erratic than what you see - they get smoothed out by the software, so I'm curious what your raw readings look like. Can you select "Export Measurements..." and post the file?
Are you getting a consistent shape from one calibration to the next? You could try reading the exact same sheet twice by doing two calibrations but using the first sheet when it wants the second one.
I'm surprised there aren't obvious quality problems. I wonder if it's silently rejecting the calibration because there are areas of negative slope (which would mathematically yield multiple outputs for a single input when you try to compensate based on the curve). In the first window that appears when you click "Calibrate," is the date of the last calibration earlier than you would expect?