Sounds to me like you have deflection/movement in your subfloor/walls or the tile adhesive was either defective, improper type, or installed incorrectly. If the loose grout is the result of movement then the tiles will need to be removed and the subfloor built up to industry standards with the proper substrate.
Otherwise you might get away with a tile repair and regrouting, although (assuming the tiles are loose which you didn't mention) the odds of other tiles coming loose are high.
Need more info on your floor/walls- subfloor thickness and type (plywood, OSB, etc.), joist/stud spacing, ceramic tile backerboard used(if any), tile adhesive used in order to offer a sound solution to your loose grout problem.