The button is implemented in exactly the same way on both pages. The only difference (besides the content of course) between the pages is the URL format. The URL of the page with the malfunctioning counter has a trailing slash:
Could the trailing slash be the problem?
Also, when hovering over the tweeted URL over at my Twitter account, Twitter shows the URL of our site´s 404-page in the tooltip. To me that suggests that Twitter has altered the tweeted URL somehow.