From what I know MobaMingle shut-down because the site did not have enough members and DeNA was not getting enough profit from the site. They just spent a lot of money but didn't get enough back.
So when they bought IceBreaker(owner of BigCafe) they just decided that maybe that would help them get the $$$ that they wanted. Then they tried to get us members migrate to that site but I think that they failed at doing it.
I honestly don't see BigCafe up for too long, I give it 2 years the most and it'll be shut-down also.
Chat with our AI personalities
Your game shuts down when someone (usually the Admins or the Owner) decide to shut it down for what ever reason they though fit. Also there are scripts that can shut it down or people can hack and shut it down.
It was temporarily shut down to protest SOPA and PIPA.
Yes the me2 universe website is shut down.
Yes. It has been shut down as of June 7, 2013.
Nothing Toxic has been shut down since 2011.