[allturtles]

I felt like none of this really paid off. Peggy has a child, that should be a life-changing event, but it's just ignored for the rest of the show because it's not convenient for where the writers wanted to take her character, I guess? I have to agree with other commenters that the show was stylistically impressive but dramatically hollow.

[twoodfin]

It is life-changing, and echoes in Peggy’s character and relationships through the entire series, as well as being called out explicitly at half a dozen key moments.

Peggy’s baby is a crystallization of the contrast between her and Don. Don tells her, “It will shock you how much this never happened.” He is always running, ignoring what life repeatedly tries to teach him. Peggy makes the decision to give up her baby the keystone of her character: She could have had Pete and the life of an adoring housewife, instead she embraced her choice and consciously took a different path.

What the writers resisted was the potential melodrama of reintroducing the baby to Peggy’s life in some way. But that would have undermined the moment of Peggy’s choice: It was gone.

[allturtles]

That's all very tidy, but what you've described is barely in the show at all.

Until reading your comment my recollection was that she left it with her sister; apparently that's wrong and you can figure out what really happened by piecing together a few different short scenes across several seasons. As someone who watched the show as it came out over 8 years, it was like the baby fell off the face of the earth with no explanation.

[twoodfin]

The baby did fall off the face of (Peggy’s) earth. She gave it up shortly after it was born. That’s it.

As I said, it comes up again and again. Most directly in “Meditations in an Emergency”, wherein she tells Pete the whole story of his baby and why she gave it up.