I just browsed to blog posts on either websites. When clicking the Tweet Button, I was able to send a Tweet. From this, I guess you mean that the Tweet Button no longer shows how often this link was tweeted.
This is expected behaviour. On 20 November 2015, Twitter has discontinued the tweet count endpoint. The backend system where the corresponding data had been stored (Cassandra database) was superseded by a more future-proof system (Manhattan). Group Product Manager @miradu explained:
Additionally, the “count API” has never existed as part of our public, supported and documented API endpoints; it was only intended for use by our own web widgets. We’ve often cautioned in our developer forums that use of such undocumented endpoints shouldn’t be relied upon, as we cannot commit to supporting them.
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