One of the little known - yet important - facts of web design is that web designers usually won't update a website they haven't designed themselves.
This is because they are so many different ways to code or create a website (i.e. CSS and XHTML, PHP, etc.). And within that, each designer has their own style of coding. Thus, even if you find another designer that specializes in your site's coding language, he or she still has to figure out how, exactly, everything is working, just to make simple updates.
As you can imagine, that takes a lot of time - too much time. From a business standpoint, it simply doesn't make sense. Which is why you'd be hard pressed to find a web designer that updates sites they haven't designed.
So if you're a business that wants a web designer who will make updates to the site after its complete, make sure and ask at the onset if they offer maintenance packages. (Not all web designers do.) If they don't, bear in mind that finding another designer down the road to do updates isn't highly likely. It might behoove you to find another designer altogether, or find a designer that will create a website you can update on your own.