The abdominal muscles are separated to remove the baby at the time of a C-section. In some cases they are actually cut, but most often, the natural elongation of the rectus muscles (the long muscles running down either side of the midline of your abdomen) can be used to just cut their middle joining ligament and then spread apart to allow for room for the baby. This muscle's blood supply and some of the nerve supply is now divided from this technique. The muscle itself has blood supply and nerve supply per segments, so it's unlikely to ever damage the entire muscle's supply. However, the lack of blood and nerve function, even to a segment, can lead to poor healing of that section, sometimes a bit more pain, and occasionally less function that before (not as flat a tummy!).
Any time a muscle has been cut, there is a chance of a hernia developing in the region after a surgery. In midline incisions (up and down, not the traditional pfannenstiel) with older studies they used to quote about a 7% chance of a hernia developing at some future date in that surgical incision. We know the hernia rates from pfannenstiel incisions are much less, but persistent pain, distended abdomens, and inability to strengthen those muscles might all be a sign of a small hernia even if one is not obvious.
There are other important layers that have to heal as well, so this is not a complete discussion of the healing after a C-section. Most women who have had a C-section may have a stitch or two placed in their muscles to close the separation that was created when entering to get the baby delivered. These stitches are typically of a resorbable nature, some of delayed absorption. It would be rare for an obstetrician to have used permanent suture, but we are encountering more permanent suture in repairs done for tummy tucks.
The absorption of the suture material occurs over time, the stitches for the ones usually used at C-section are weakened to about 50% of their strength at about 2 weeks, and it takes much longer to completely dissolve. So minor nerve entrapment around the muscle usually begins to resolve as the sutures weaken, so at about 2 weeks, barring infection or any more dramatic swelling. So when we say “the muscles” as usual, we mean a whole lot more: the pregnancy, the surgery, the healing, the care we have taken of our bodies, and the shape we get into afterward. It’s a great subject to gab with your gyno about.