The button anchor is a relatively new device used in rotator cuff surgery. Studies have explored the concerns you describe. So far, there have been no cases of anchor pullout or loosening in the first year after surgery. Likewise, there have been no cases of bone infection from the anchor that could lead to weakening of the bone and pullout. The complications reported have been movement of the anchor or breakage of the suture where it’s tied to the anchor.
Several studies were done before these anchors were approved for human use. Doctors inserted the anchors into human cadavers (bodies preserved for study) and then into live pigs. In both groups, the anchors were stressed with thousands of repeated movements. Doctors do these kinds of tests to make sure a treatment is safe before using it on humans.