The accepted practice for installing floor tile is to have a 1 1/4 inch minimum underlayment installed prior to installing ceramic floor tile. This means, if you have the typical 3/4 inch plywood subfloor, you indeed needed to add either 1/2 inch plywood or 1/2 inch Durock to reduce deflection of the subfloor. Failure to do this results in the cracked grout you are experiencing. Also, there is a product called "Flex-Set" that is a mortar-based bedding that will withstand some movement. I would imagine there may be a grout compund that would be similar. You will need to remove the existing grout first, which is neither fun nor easy. Also, make sure you use "sanded" grout, which is for floors, and a polymer additive instead of water to increase the bond strength. Good Luck.