Whats the oldest existing bitcoin exchange around which never had problems like mt gox and is still around?
There are a lot of old exhange including poloniex bitfinex and coinbase there are also kraken too here in indonesia there is indodax and triv
And about the problem the key is that there is always a problem for centralized exchange but at some point they just improve their self like security patch and other but sometimes company like bittrex is cease to exists
Most definitely problems are bound to happen be it public ones or the ones that is faced internally. The most important as you have said is to have the flexibility as a company to continue tackling these issue and stay afloat with business which some of these old CEX have done excellently. If you even compare the rate at which some of the new CEX are closing up due to problems then you have to give credit to these veteran CEX like bitfinex and bitstamp