I have a persistent problem matching blue colors, especially a large area of blue, like a sky.
There seems to be a shift from "turquoisish" to "purplish", i.e. blue + green to blue + red.
This sort of problem is usually pretty straightforward to figure out, if a little tedious. Track the color through your workflow.
[ Your biggest problem may be that you don't actually know what your workflow is in a technical, color numbers sense, and/or you are unfamiliar with the tools needed to do this. ]
i.e. Pick a uniform reference patch in the original. Measure it with your instrument. Scan it with your scanner.
Check the delta E and the error direction between what you measured and what the scanner profile predicts it will be using Absolute colorimetric. If that looks OK, move to the next step in you workflow.
If you are doing (say) a relative colorimetric to relative colorimetric conversion from scanner to printer then:
Convert the scanner RGB to relative (PCS) L*a*b* using the scanner profile relative colorimetric forward table. Convert that number to the printer "RGB" space using the printer profile relative colorimetric backwards table.
Check the printer profile invertibility/clipping by running that RGB forward through the printer profile using relative colorimetric, and check the resulting L*a*b* against the one you put in above.
Print a patch with that RGB. Measure it with your instrument.
Use the printer profile to convert the printer RGB to Absolute colorimetric L*a*b* using the forward table, and check the delta E to what you measured on the printer.
That's about it really. The source of your problems should show up there somewhere.
If the above indicates there is no problem (the delta E's are small and don't compound), then perhaps there is a difference between your actual workflow and the above manual one. You can do a similar exercise by comparing various values between files through your actual workflow and the manually calculated numbers.
Typically I would use ArgyllCMS icclu to do these profile conversions (of course!) - but maybe other tools could be used if they are more familiar (ColorThink ? Photoshop if you configure it properly ?).