Cycle through fonts does not work

Does it always get stuck on the same font?

If so: which one?

Do you have font management running?

Did this problem just start happening or has it been occurring for some time? Have you installed any fonts lately and what kind? Certain kinds of fonts can really gum up in-menu preview renderings of font styles. Picture fonts (font files that contain pieces of clip art as glyphs) tend to be the worst. Badly authored fonts can also cause problems.

You could try disabling in-menu font previews in Illustrator Preferences (look under the type section). I'd recommend looking at any recently added fonts and removing them temporarily and then adding them back one by one to narrow it down to the culprit.