He seems honest but 19,980 bitcoins are missing. That's roughly $270,000 worth. I just don't see how it can survive that.
To put things in perspective, Gox makes about 10k btc a month. Bitmarket is no Gox, so it would take them longer than 2 months to recover from this, but it's not impossible. Hopefully they can get some investors to bail them out a bit, but it is possible that they can survive this.
I for one hope they do.