I have 27 identically sized charts that I created in Excel 2007. All
but 2 of them auto-wrapped the x-axis titles correctly. On the two
bad charts the titles overrun each other.

How the heck can I get these 2 misfits to conform?

I can't find the setting on the Format Axis options and the Wrap Text
button (under Home Alignment) is grayed out.

As far as I can see, there is no difference in any chart settings
between the good charts and the bad one.