In Bendless Love, Bender recounts his birth four years prior. He was born in a factory in Tijuana, and his mother is shown to be a giant robotic arm. This story holds in several other episodes. In The Bots and the Bees, Bender tells his bastard son, Ben, that he's a great bender because he inherited his arm-control software from his mother. In the movie they showed Bender at the robot teen center, they said that in addition to being put together in a factory, robots could have babies to keep up with consumer demand. Bender was still made in a factory, it was his SON that was conceived by robots.
I haven't read any other theories, or if Futurama had a fix for this, but
HERE IS MY THEORY TO FIX BENDER'S ADULT BIRTH AND BABY BIRTH:
In Lethal Inspection, we see a young Hermes approving robots on an assembly line. Baby Bender comes along, and despite his being defective, Hermes still approves him. However, like I said before, we are shown Bender being born as a fully grown robot in Bendless Love just four years prior.
Look at how young Hermes looks in that flashback (or just Google "Bender baby"): http://pichars.org/store/6343_original_2Isi6.gif
Hermes Conrad was born in 2959, making him well over 50 by the time he and Bender go looking for Inspector 5. Let's say Hermes is 30 years old in this flashback, which would mean Bender was REALLY born over 20 years ago!
So how is he born again in the Bendless Love flashblack?
In Lethal Inspection, after the Sith War reenactment, Bender is telling everyone how he just uploads into a new bending unit body if he died in his own. What if Bender died in the body (or bodies) before the adult birth we saw four years ago? He would have uploaded into the Bender body that we all know and love.
But he's defective and can't upload into a new body, that's the point.
I know this part is a bit reaching, but that's why it's a theory. We know Bender's current body is defective and he will permanently die with it. However, we don't know that his original body was defective for that reason. It could have been another problem altogether, they don't tell you!