The floor is flexing or the tiles never got properly adhered. There are tile experts on this forum, but I suspect the solution would be to remove the grout and the tiles, clean up the old thinset, then re-lay replacement tiles.
However, if the floor is flexing, this problem could reoccur. Basic Principle: rigid tile does poorly on a flexible underlayment. That is why we use Hardie Board on the floor to stiffen it.
It's laid on backer board which is laid on a subfloor underneath that. I can post a pic. It's a crawlspace underneath the floor.
When looking at the joists, check the size 2x8s, 2x10, or what? distance apart 14 1/2", 22 1/2" ot what and how long are they. Then you want to look for noticable damage, big knot with carcks extentending to the bottom or top, notches cut out of the joists for plumbing, holes drilled for wiring really close to the bottum edge of the joists.
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