It could be lotsa things; lack of support, the floor under that tile starting to rot, insufficient mortar under the middle of the tile, a defective tile having been put in, etc.
However, if I had to guess, my best guess would be that either someone used fir plywood instead of fir underlayment on that floor, or that it's a soft spot in the cement board that was used as the tiling substrate.
But, there's a good chance it's because whomever set those tiles pulled up the old underlayment rather than remove the old flooring that was glued down to it, and replaced it with plywood instead of fir underlayment.
Now, 1/4 inch thick plywood and 1/4 inch thick fir underlayment look the same. The difference is that plywood is allowed to have voids in the middle ply(s), whereas in fir underlayment the voids that are allowed are very much smaller or they are filled in with water putty in the manufacturing process. That's cuz such voids will cause "soft spots" if the plywood is used as underlayment on a floor.
It isn't often that this happens with ceramic tile floors cuz the tiles are larger and stronger. Where it's more of a problem is with sheet vinyl and VCT tile flooring where you get a "depression" forming on the floor.
Now, that's a very possible cause if the tiling was done by the previous home owner, but no professional would ever set tile directly over plywood or wood underlayment.
The reason why is that wood is a natural material and swells and shrinks with changes in it's moisture content caused by seasonal changes in humidity. Because of the way it's made, plywood (or underlayment) has less dimensional change than lumber, but it's still not a suitable substrate to tile over. Ceramic tile mortar and grout simply don't have the elasticity to accomodate any movement of a wood substrate, and so if the wood ever gets wet, then the predictable result is cracked grout lines in the floor.
A pro would always put down cement board panels over any wood substrate before tiling. The cement board is dimensionally stable and doesn't swell or shrink if it gets wet, thereby denying the grout any excuse to crack. And, it's that dimensional stability that mades cement board panels suitable as a substrate for ceramic tile.
The problem is that not all cement board panels are made equal.
Wonderboard is better now than it used to be, but my experience with Wonderboard panels 10 or 15 years ago is that some areas of the same panel would be hard as granite, and other areas simply didn't get properly filled with cement and the area would be so soft you could just about crush it with your hands. If you put a floor tile over that spot, I can see that it could very well crack due to lack of support.
Another product, called "Durock", was made much the same way as Wonderboard (with cement aggregate sandwiched between two layers of fiberglass mesh), but I don't recall if Durock was any better in terms of consistancy or not. "Hardibacker" is uniform in strength and hardness throughout the panel, and it's the only thing I'd use for a ceramic tile floor. Dens-Shield is uniform in strength and hardness, but it has a gypsum core instead of cement, so it's not as hard as the other tiling substrates and I wouldn't use it on a floor for that reason alone.
So, it could be 100 other things, but in my view, it's most probably a soft spot in any plywood used as underlayment on that floor or a soft spot in any cement board panels used as the tiling substrate on that floor. (And, so far as I can recall now, Wonderboard was the most notorious for the panels not being of uniform strength and hardness.)
Let's see what other people think.