Is there a constant risk of infection with infraorbital rim implants, or is the risk period only in the initial few weeks?

Any artificial material in the body has a risk of infection especially if porous.  This is even true for liquid implants like fillers. Although the greatest risk is in the first several weeks after surgery (usually from intraoperatuve  contamination), future circulating infections can settle in the implanted material. Because the face has good circulation, it less likely to have an  initial  infection compared to other parts of the body.   But precautions should always be taken to minimize the risk with implants. The risk with a solid silicone is low and these implants can  be fairly easily removed if necessary making them a common choice. 

The risk of infection is highest in the initial weeks of the surgery although much less risk remains throughout the life of the implant. 

All foreign implants have a risk of infection. Infection does not always come from the surgery itself. With regards to the face, there is relatively a small risk of an acute infection following surgery. Appropriate precautions should be taken before and after surgery to prevent any occurrence of infection.