Code : Twitter did not return a recognized response code.

First, you should verify that you’re using HTTPS. It’s under the Error Messages & Debugging section of the WP to Twitter settings.

An unrecognized response code means that your server was unable to reach Twitter at all, so it did not receive a response. This can happen for many reasons, but if you’ve been able to use WP to Twitter in the past, it may be a temporary situation. If you’ve made any server changes recently, however, it may be worth reviewing those, in case they broke something related to making remote requests.

I`m using https. The plugin worked until this morning (10 in the morning, GMT+2).
I`m not sure what do I need to install (if any) on my server. I read various websites that specified CURL SSL, which I checked in apache config and is installed.

That should be sufficient, but there still could be other reasons – Twitter blocking your server or c-block of IPs, etc.

Can your server contact other external services, such as the WordPress plug-in API, to install new plug-ins?

Seems that there was a problem with my server contacting external services. I could not update or install any plugin. Now it`s all back to normal, thanks for the support.

By the way, as a future feature request: Can you make an option to skip just once (basically this time) the twitter update for a post?

Thanks

You can already do that – just flip the option to not Tweet the post in the WP to Twitter meta box when you publish.

I know that, but that option will be checked next time. I manage like 5000 posts and update many of them at a daily basis. 99% of the cases I forgot which one I checked not to tweet and Im too lazy to check the meta box each time. So just a "dont tweet this time” radio button will be really cool.