Tiles - Grouting

Could be all sorts of reasons for the tiles moving and could be impossible to fix without replacing the floor, but if you want to try something fairly simple look up Fix a Floor on google and give it a go. This may not be a permanent solution and you may end up having to relay the floor in time but might buy you some time. Might also be worth checking for leaks. Water getting under the tiles could be one reason for them being loose.

Rip up and start again using the proper method

Grout becomes loose only because the tiles have not been fitted correctly, you must use flexible adhesive to lay porcelain on concrete floors and wood floors, before you lay any floor tiles in an upstairs bathroom you must ply the floor, if the ply is not screwed down properly and there is movement in the tiles and adhesive, this will crack the grout, so basically it’s pointless re-grouting, the whole floor will need to be done again

Grout flaking and any movement of tiles is a clear indication the tile project has not been prepared properly and certainly not been laid properly. It's all to do with what the tiles have been laid on to and the materials used. Sadly, there is really only one true way to put this right and that is to rip everything up and start all over again. I know it's not what you want to read but it's the only proper way. Good luck.