Twitter --> Error: 0 - Bad request token!

The 3 most common causes of that issue are:
1) Your server time is incorrect - this doesn't look to be the case from what I can tell
2) Your Twitter Application wasn't set up properly
3) You didn't copy the API Key and Secret properly to JFBConnect

I'd suggest double checking #2 & 3 and going through the Twitter Application Setup guide for Joomla again.

If that doesn't help we'll gladly try to help investigate further, but I don't see any immediate causes.

One final question: You've been a subscriber for some time. Was Twitter ever setup and it just started failing, or is this the first time you tried? Knowing that will help give direction on where to start.

Thanks,
Alex