Is it by any chance a K3 in one of the Amazon covers that clip into the side of the Kindle? If so, I would try removing it from the cover and use it for awhile, and see if the problem stops. If so, contact Amazon CS and tell them you want credit toward a new, non-Amazon cover.
Otherwise, you could do the usual check to see if there is an indexing problem (at the home screen, search for a nonsense phrase and see if any books come up as not indexed (cannot be searched)). It's possible that if there is a problem with an item, the extra processing load of continually trying to index it might be overloading memory or such. If so, delete the offending book(s), and see if that clears things up. (You can then try re-downloading it to see if a fresh copy fixes it.)
If it's neither of those and no one has a better suggestion, I'd call/write Kindle CS and see if they want to try any sort of firmware update, or just send a replacement. Or perhaps if it's too far out of warranty, they may at least offer a deep discount on a new one.