The nearby and young M star AU Mic is surrounded by a debris disk in which we previously identified a series of large-scale arch-like structures that have never been seen before in any other debris disk and that move outward at high velocities. We initiated a monitoring program with the following objectives: 1) track the location of the structures and better constrain their projected speeds, 2) search for new features emerging closer in, and ultimately 3) understand the mechanism responsible for the motion and production of the disk features. AU Mic was observed at 11 different epochs between August 2014 and October 2017 with the IR camera and spectrograph of SPHERE. These high-contrast imaging data were processed with a variety of angular, spectral, and polarimetric differential imaging techniques to reveal the faintest structures in the disk. We measured the projected separations of the features in a systematic way for all epochs. We also applied the very same measurements to older observations from the Hubble Space Telescope (HST) with the visible cameras STIS and ACS. The main outcomes of this work are 1) the recovery of the five southeastern broad arch-like structures we identified in our first study, and confirmation of their fast motion (projected speed in the range 4-12 km/s); 2) the confirmation that the very first structures observed in 2004 with ACS are indeed connected to those observed later with STIS and now SPHERE; 3) the discovery of two new very compact structures at the northwest side of the disk (at 0.40" and 0.55" in May 2015) that move to the southeast at low speed; and 4) the identification of a new arch-like structure that might be emerging at the southeast side at about 0.4" from the star (as of May 2016). Abridged.