I don't think Bitstamp is going to disappear overnight like Mt. Gox. They've got a lot to lose.
The company has generally been respected within the bitcoin community. In May 2014 it passed a proof-of-bitcoin-reserves audit overseen by BitcoinJ developer Mike Hearn, and in June it beat other bitcoin companies to win the Europas' Best Virtual Currency Startup Award.
A lesson learned from the whole Mt.Gox debacle is that they need to keep communicating. This doesn't seem to be a priority at the moment. I'm still wondering where that statement on coindesk came from. It isn't on their website or twitter. So how would customers know (apart from reading coindesk).
Having said that I don't think they'll go bust because of this. I've been using them since long before Mt.Gox started to slide and they've proven to be a reputable exchange.