Depending on the style of beer, you can see suspended yeast in the bottle for anywhere from 3 weeks to several months. Higher the ABV, the longer the bottle will take to finish carbonating. As long as you see suspended yeast in the bottle, the yeast is munching away at available sugars.
Sertain styles and their associated yeasts can also be a factor. For example: a Hefeweizen will not usually clear up in the bottle, as the style of yeast does not flocculate as much (clump and settle to the bottom).