I usually find that if the grout around a tile is cracked, the tile is probably loose. If the tile is loose, it can be pulled up and reset then regrouted.

I sometimes lay wood floor over existing tile so cracked grout is a warning sign indicating loose tile.

Thanks for the reply. In this case, the tiles do not seem to be that loose. Obviously there is a space under the hollow sounding part of the tile, but that is generally little or none, up to ~15-20% on several tiles, and nearly 50% of one. It is as though the tile is mostly well adhered, and detached along one side, the same side as the grout crack. If any spares were available, I'd be trying to remove a couple of tiles, but I cannot risk breaking a tile and having to replace 600 square feet.

Some similar issues were fixed a while back (grout was removed and replaced), but no hollow sound was noticed at the time.

Hmm. It's probably either small voids under the tiles which are inconsequential or maybe the adhesive has popped loose from a poorly prepared portion of the subfloor. I think they make kits to shoot epoxy under tiles voids but that sounds a bit risky. Maybe if the cracked grout was removed a thin consistency two part epoxy could be poured in at the edge of the tile then grouted over after it cures.

Just saw this-the voids can be filled with latex.
super latex from latticrete works well.
However it may be a good idea to hire a pro to pump in the latex. also there is an epoxy made by bon stone in an injectable syringe that will work very well.