"Brain Teaser"

I don't expect an answer, but feel free to send me an E-mail if you like. Maybe an engineer somewhere has an idea.

Let's suppose somebody could build a six foot tall robot. And... this robot could build another robot half it's size with the same manufacturing ability as the six foot robot. Then, the three foot robot builds a one and a half foot robot, etc.

At what point would the new robot be too small to function?