We recently put down a new bathroom floor with blue grout. Since that time our bath mats have a terrible mildew smell. We keep cleaning then and finally replacing them. All I can think is that the mildew must be in the grout. There's no discoloration, though. What can I clean the bathroom floor with that won't discolor the grout?

You may get mildew ON grout but rarely IN it. Grout is pretty hard stuff and impervious to most chemicals but do a test first. Behind the toilet do a test drop of straight bleach. After 10 minutes if it has not discolored the grout then wash the floor with a 1:4 mix of bleach and water. Allow it sit for a few minutes and rinse 2-3 times. What is your sub floor beneath the grout and is this on or below grade?

THanks for your response. I don't know what's underneath the floor. It's an old house. It's on grade.
I'll try your suggestion. Have you any other idea of why all my mats would be mildewing?

You meed a exhaust fan in the bathroom or open a window to let the humidity out.

This May Sound Silly ,but Is It Possible Someone Washed The Rugs And Didn't Dry Them Soon Enough, That Will Give You The Smell, And Ive You Had Mildew On Or In The Grout You Should Be Able To See It.
If You Think Its In The Grout, Do As Ballenger Said And Ive It Doesn't Mess With The Color , Id Seal The Grout.
However I Really Don't See This Being A Grout Problem.

As Far As An Exhaust Fan, That's A Good Idea If There Are A lot Of Showers Being Taken, Hot Steamy Showers Can Definitely Soak Some Rugs, And If They Just Sit There Wet They'll Mildew.

I do have an exhaust fan and it runs every time we shower.
At this point, I'm positive the problem isn't the mat. I've bought about 4 new ones since we've had the floor done. The problem keeps happening. We do hang the mat over the curtain rod every time, but it still smells.
The only think I can think of is the floor. The room actually doesn't smell, it's just the mat that's been on the floor.
Any other ideas? I'm stymied.

You said in one post that this room is on grade. Is it concrete on grade? If so you are probably getting condensation on the tile because concrete on grade is very cool, can be cold. It isn't hard for the tile and air to hit the dew point and condense. Continual dampness will result in mildew and/or mold.