Kludge of a workaround, but if I was using a Twitter app with older links that work but newer ones that didn't, I'd start off with the most recent tweets, happily use the older link to scroll back through tweets and on the rare occasions I want to go back to newer tweets, curse the broken newer button - and use the browser's back button instead to return to the pages I'd viewed earlier which had the newer tweets.

So (a) having only a working older link isn't that bad, and (b) rather than pulling data from Twitter, couldn't you use that cached information that the back button uses?