I had light colored grout on my kitchen floor tiles that was filthy. I scrubbed, and sealed it several times. While that worked for a few months each time, it just had too much traffic and didn't take long to look bad.
Tile experts told me the only solution was to change the grout. Cut the old out and put a darker grout in. It was to be an expensive job.
Believe it or not, I decided to try staining the grout instead. I used a concrete stain and tinted it to a burgany color. The grout still looks great today, and the stain works as a permanent sealer. That was 12 years ago!