There is a sanded grout where tile meets the wood. It's working nicely.
We have been talking reinforcement in the joists( the basement underneath is unfinished) and my builder felt there wasn't enough play or movement to warrant adding supports.

http://www.johnbridge.com/vbulletin/deflecto.pl

We have 'I' beam joists, can't use this calculator

The deflection of the I joists should be on the home's blueprints and materials schedules. The lowest deflection that satisfies code only supports carpet as flooring. Builders generally comply with code, bt not one whit better. You need an engineer to design reinforcing to stiffen the floor.

Sophie's quite right...tiles must be specified on architectural designs before the project is built. What I'm seeing is straight line cracking along an entire tile (from the photos) which would point to movement/floor flexion issues rather than grout failure. It looks like this floor is pitching/heaving so much (too flexible...not stiff enough for tile) to cause entire rows of tile to rip away from the grout. Kinda like how you crack and bend the ice cube tray to get the cubes out. The more you twist and bend the tray, the more the cubes "let go" of the edges of the tray = loose ice. I would bet the same thing is happening here.

The only other "thing" you can look at = cleaning products. What works for wood is HORRIBLE for tile and what works for tile is DISASTEROUS for wood. That is the other vein...but I believe you have too much flexion in your subfloor.

I would ask to get a second opinion. If your builder was the one who didn't think you needed reinforcement, then I would ask for a second set of eyes to look at this. If the joists are open, then this might have an easy solution (not cheap...just easy).

I realize i may be a little bit late responding to this but they're may not be deflection in the sub floor. It could be much simpler than that. The grout is coming out because the time is moving. How ever the time corks be moving due to lack of mortar coverage on the back of the tile. Or it could be the way the durock is installed. It it's supposed to be installed over thin set and fastened with screws. A LOT of installers out there use nails to save on time. Either way the tile does have to be removed and replaced. As long as your sub floor is at least ¾" thick and the joists are no further than 19.2" o.c then additional blocking is not needed

I apologize for the grammatical errors. Auto correct and big thumbs don't mix on a phone

Thanks for your reply and I’m happy to report that we discovered a solution. After removing the traditional grout four times, we discovered Snapstone flexible grout. It was an immediate success and has held up like a champ to this day. It’s a great product that is easy to use.
It may well be that all of the above repair suggestions were correct but our builder did not,and were unwilling to do any more work. Finding an engineer and tearing up the installation was not an option, more likely we would have just put in wood flooring throughout.