Aren’t they rejected sometimes?

There is no immunologic rejection of titanium implants. Commercially pure titanium is perfectly biocompatible and is accepted by the organism. This does not mean that it has a 100% success rate, but a failure is manifested as light mobility and a sensitivity around the implant. The implant is removed in such situations and may be replaced with another implant after healing. Inflammatory reactions (osteitis) leading to substantial pain are extremely rare.