Actually, I do see your support request; and I responded 3 days ago. This was my response at that time:
You're not getting any errors at all? Hmmm. That's interesting. Do you
see any messages on the published posts that were not Tweeted in the
'Custom Tweet' meta box provided by WP to Twitter?
I notice that your site is loading pretty slowly; that makes me wonder
whether you're having a memory issue, but there's nothing definitive
that I can point to. You can try increasing the PHP memory available
to WordPress, however -- here's a tutorial on that:
It may be that your server is running out of memory while trying to
post to Twitter, and if it runs out of memory it can neither post to
Twitter nor produce an error message.
Disabling register globals wouldn't have any impact on WP to Twitter, however.