There are two colors that are pain in the part of your back when they lost it name.
First is called "Money color" or green.
Second one is "Tomato" or red.
Both of these look good on screen but in print, because is made from mixing two paints, it can easily shift to different color.
So what to do? There are profiles set up exactly for that purpose where they try to keep red or green (not both though) as vibrant as they can. Those profiles can be shipped with specific machines as offset printing and solvent have different specification.
And at the and, as always, I encourage you to read great book by Dan Margulis that cover all those problems when you want/need to adjust the photos or materials manually.
And consult with your printer about his method and don't be afraid of preparing cromalin with different settings.
Remember, sometimes watching at printout in office or natural light can make the difference.