The table service restaurants generally change a few items with every change of the season (roughly beginning of June, beginning of Sept, beginning of Dec, beginning of March), with a few not changing much and a few changing quite a bit.
As for the counter service, they stick with what's popular - if something's not selling, there's no reason to keep it.
For Ohana and other buffets, the restaurant is always busy, but they keep track of what people eat and reorder, and go by that for popularity. The rice may not have been very popular. I rarely ate the rice when we went to Ohana, for example, because I thought it was pretty flavorless. I'd probably prefer cheesy potatoes.
Edit: of course, they make changes for other reasons as well, but probably not as often as the above reasons. The Garden Grill, for example, I don't believe they changed that to the new, weird, "upscale" menu because of a lack of popularity.