Ender 3 nozzle gets closer and closer to the previous layer as the print progresses
Finally I've found the damn problem: Adjustable rollers of all axes were flat on one point making layers to shift in all directions.

The effect was less visible on the X and Y axes but it was more notable in the Z axis as the flat part was right from the start of the print. I think that flat part was making difficult for the Z axis to move upward, and making my prints fail when printing at higher resolutions (I guess the finer the displacement the weaker the torque).

It seemed to me that the nozzle was getting closer to the previous layer but instead it was resting (or barely moving) on the flat part of the Z right adjustable roller first and then on the other adjustable roller of the same axis.

To diagnose the problem disable the steppers and moved the axes manually and feel if there are notches, so to speak, in various spots on every axis.

The solution is to replace the rollers with new ones and to not close them too tight otherwise they'll deform over time.