Wifey and I have used Oxy-bleach -- a specialty brand used by contractors that usually cleans everything quite well, no luck (and Oxy-bleach is NOT the name of the product).It is much better than most of the supermarket brands.
I used a special Clorox brand cleaning solution recommended by Bob Villa, no luck. Used baking soda. Used two or three speciality grout cleaners that were quite expensive, no luck.
I really am reluctant to use straight bleach, but may try it. My mom used to use it.
But, I bought a scrubbing stone awhile back that is made from recycled products, not as abrasive as the pumice stones. I used it on stubborn toilet bowl rings that had been around for a few years and had resisted all attempts -- and with little effort, the rings were gone -- quickly --- I may give that a try this weekend. It would probably cost some $50 in total to do our two bathroom floors with the scrubbers, but cheaper than calling someone in.
And, yes, supposedly the grout was "sealed" with protectant when it was installed.