I have ran into this problem before! There is some package or something you have to enable to be able to use the mm notation. I will try to remember what it is (although someone might beat me to the punch).
Hmm, this seems to be particular to the PyPlot backend. Other backends increase the margin between the label and axis but PyPlot pads below the label instead. If you try another backend (GR, Plotly, etc.) you can do what you want.