Do permanent sutures ever get rejected from the body as they are a foreign substance?

Thanks for your question. You are completely correct. The scar tissue which forms after abdominal plication holds things together. After some time, the permanent sutures become superfluous, or worse, a nidus for infection. Sutures should function like a house painter. They should do their job and then leave. Over the years, my practice has changes such that I prefer PDS sutures. They remain strong for months and slowly degrade. But in reality, surgeon preference is a personal thing, based on continuous study, and experience. I would not fault my colleagues for holding a different preference. If you are in search for a plastic surgeon to perform your abdominoplasty, feel free to ask their preferences and why they hold them. They should be frank.

I believe this problem refers to rectus abdominis muscle, and due to the tension that can be applied to the muscle during exercise and lifting, a lot of surgeons believe that permanent stitches will be more suitable. 

Hi and welcome to our forum!
Debate continues over the years regarding suture selection in rectus muscle repair.
Non-absorbable sutures are usually reliable, maintaining tensile strength until scarring strength has reached its maximum. However, in some patients, an indolent infection may cause the suture to "spit". An inflammatory reaction drives the suture to the surface unless tethered by a deep structure in which case, there may be development of a sinus tract from skin to suture, requiring manual extraction. 
Absorbable sutures are somewhat unreliable as dissolution rates may vary from individual to individual. Rapid absorption before wound strength is sufficient may result in suture line disruption.
Plastic surgeons are divided as to which is best...They base their decisions upon their lifelong experience.
Visit a board certified plastic surgeon for evaluation and discussion.
Best wishes...