Socks usually wear by mechanical friction: with your feet, and with the outside environment (shoes, floors, beds...).

Now what you describe is obvious: the heel takes the hardest physical in the body, which generates two favorable conditions for your socks to wear:

1. The sock is repeatedly crushed between your heel and floor / shoe.
2. The skin on the heel tends to become thicker and coarser, compared to the skin on other parts of the body.

Now it is easier to find ways to extend the life of the socks:

• make sure that the shoes that you wear are smooth on the inside;
• make sure that the foot applies uniform pressure on the inside of the shoe; otherwise, the parts of the socks getting the higher pressure / friction will die first;
• make sure you have a proper skin care, especially in the heels area. Make sure that skin is soft and smooth.
• wear some additional shoes / socks / whatever, which will take the most part of the abuse; either the additional footwear is more resistant to wear (like shoes), or is cheaper to replace them.

Once the material / fabric of the sock is gone, there is very little that can be done to revive it.

Socks usually wear by mechanical friction: with your feet, and with the outside environment (shoes, floors, beds...).

Now what you describe is obvious: the heel takes the hardest physical in the body, which generates two favorable conditions for your socks to wear:

1. The sock is repeatedly crushed between your heel and floor / shoe.
2. The skin on the heel tends to become thicker and coarser, compared to the skin on other parts of the body.

Now it is easier to find ways to extend the life of the socks:

• make sure that the shoes that you wear are smooth on the inside;
• make sure that the foot applies uniform pressure on the inside of the shoe; otherwise, the parts of the socks getting the higher pressure / friction will die first;
• make sure you have a proper skin care, especially in the heels area. Make sure that skin is soft and smooth.
• wear some additional shoes / socks / whatever, which will take the most part of the abuse; either the additional footwear is more resistant to wear (like shoes), or is cheaper to replace them.

Once the material / fabric of the sock is gone, there is very little that can be done to revive it.

The way I see it, if a repair is done, it will either look bad, or it will be uncomfortable to wear. Or both.

Your question sounds similar to:

How can I prolong the life of a kitchen plate, after it has got a hole in the bottom?

Maybe as a frisbee?

Brainstorming: if the socks are long (they go up on the leg high enough), you might just cut the worn part out, close the cut by sewing, keep wearing them (obviously, they will be shorter this time). A new heel will form by itself, even though they might be slightly less comfortable to wear (compared to new socks).