It may appear that plots C and D are not log y-axis, but that's only because MATLAB doesn't draw the small ticks under certain conditions (depending on the axes height and ylimits). They are still log-scale, they just don't show the small tick marks between the decades.
For example, with this figure size (height: 1000 pixels) plots C and D do not show the small ticks:
figure('Position',[1 1 1000 1000])
boxplots_logaxis
But with this figure size (height: 1500 pixels) plots C and D do show the small ticks (so they look like how you expect a log-scale axis should look):
figure('Position',[1 1 1000 1500])
boxplots_logaxis
Conclusion: make the figure taller in order to see the log axes ticks.
You're not going to be able to include negative values on a log-scale axis.
