Cracking grout in a newly tiled floor is a real letdown after all the work you put into it. The causes could range from a poor grout mix to a lack of expansion joints, to movement of the tiled surface. If the cracking grout is concentrated in a floor's walkways, the likely culprit is floor movement, or deflection. Although it might ultimately be necessary to stiffen the floor, there is a much simpler fix you might want to try first—caulk as flexible grout.
The quick fix for cracked grout
Remove all the loose and cracked grout with a grout saw or Dremel tool and completely vacuum out the gaps. Then apply the caulk and smooth it with a wet finger or plastic spoon. Let the caulk cure for at least 48 hours before allowing anyone or anything on the floor.
At most tile specialty shops, you can get or order sanded caulk (most floor grouts are sanded) that will closely match your existing grout color. Incidentally, this fix is only practical for interior tile floors and when the gaps between the tiles are 1/4-in. wide or less.
Ultimately, you may still need to stiffen the floor, but in many cases, using sanded caulk will work and save you money and grief.