As Fedya notes, "Baby" is relatively cheap to produce. It also had big-name sponsors in P&G and Walmart for Season 1. Bringing them both back to the fold (or a similar sponsor -- say, Target instead of Walmart) probably guaranteed them a second season.
It will likely air again on Saturdays during the spring or summer, although it wouldn't hurt ABC to try the show on Fridays at 8pm ET before "Shark Tank" once "Last Man Standing" and "The Neighbors" end their seasons. "Shark Tank" has a very strong following not just with the key 18-49 demo, but also with families (The ABC programming chief mentioned in the fall schedule announcement in May that "ST" is, in his words, "the most popular ABC prime time show with children"). It's a longshot, but "Baby" might benefit from the "Shark Tank" pairing.
JD