Permanent Sutures for Bottomed out Correction?

What suture material was used is less important than what caused the the implant to bottom out in the first place.
Was the implant too large? Was the muscle too powerful given the resistance of the patient's tissues? Was there a larger implant in at one time and the capsule has never recovered?
If any of these problems are present, the next implant is likely to bottom out just as the first one did... no matter what sutures are used.

If one tries to recreate the inframammary fold (basically to raise it), would use permanent sutures. The kind of suture one uses does not matter, although a soft suture like goretex and braided nylon will be less palpable through the skin. These sutures are placed into the perichondrium (rib cartilage) and the deep part of the skin to define the new breast fold. I've seen these work in about 50% of the cases. The weak link is the skin, from which the suture pulls away with time especially if you have a large implant placing downward force on the suture line. Taping up the fold with microfoam tape after surgery and having the patient wear a bra 24/7 for a months, can help but it's not a guarantee. Good luck.

 Some surgeons use permanent sutures to support the breast fold. I tend to use absorbable sutures like PDS that tend to last long enough to allow the body's natural scar tissue to develop without leaving a permanent suture in. The permanent suture can be a nidus for infection.

Another option for bottoming out has been a piece of acellular tissue matrix designed to suppport tissue regeneration. It is called Strattice. This provides added support to reinforce the bottom of the implant. It is recommended for use in soft tissue repair where weakness or a deficit exists and can help in bottoming out situations.
It is somewhat new so ask your Board Certified Plastic Surgeon if he or she has experience in this.

The reason why surgeons use permanent sutures to correct a bottomed out implant, is to add one more level of long lasting strength to the repair. The sutures that you mentioned in your question are all monofillament sutures, (not braided or multiple fibers like string). This decreases the surface area and lessens the chance for a source of a chronic infection or inflammatory process. All of these sutures are theoretically non reactive so the chance of a rejection is very small. On the other hand a absorbable suture such as Vicryl promotes an inflammatory response as it dissolves and is more likely to be rejected.

I agree that the skill of yor surgeon and the health of your tissues are the most important factors in correcting bottomed out breast implants.
I also think the technique is most successful when the repair is sutured to the rib periosteum.
To answer your question I use 1-0 or 0 Prolene sutures.