Sounds like the problem lies with the mortar used between the Ditra and the tile. Schluter specs the use of "unmodified" mortar to set the tile over the Ditra. Modified mortar is used to bond the Ditra to the substrate. The Modified mortar needs air to cure. The air cannot penetrate the ditra or the tile so it stays "wet".

-Mike

Are the tiles Porcelain??
If so loads of rapid set flexi ad's don't take to porcelain very well.
So (having sorted a couple of problems that have been identical to yours) over time the tiles start to debond from the ady & work loose, then it doesn't matter how flexible the grout is (unless it's chewing gum) it'll fail.
If you've got decoupling membrane properly fixed then that kills most other problems. Use areally good ady (BAL) and butter the tile then re fix to a complete bed under.
If the tiles aren't porcelain let me know and I'll have a rethink!!! Because that would be strange!!

Sorry reading on an iPhone so you miss some of the conversation!!
The problem isn't the grout, if the tiles are moving because they aren't stuck down right the grout failing will keep happening so focus on the problem under the tiles first!

Just a question. But are you sure the decoupling membrane was Ditra? and not another brand? do you remember what colour it was?

_________________
Professional Kitchen & Bathroom Fitters | Master Painters and Decorators | Brighton & Hove