It's not uncommon for services that are growing fast to be overloaded. Twitter is a famous recent example. Empirically it seems to be a predictor of success. Off the top of my head, I can only think of one startup (Friendster) that died because it couldn't handle its own popularity, and that was a pretty extreme case.
Friendster was the extreme case because, of the poor management behind the company. For instance, they went through 4 CEO's over a short period of time and they chose to do a full rewrite from Java to PHP instead of trying to scale the service and because, the rewrite wasn't implemented properly it had to be rewrote again a couple of years later. Moreover instead of sharding/portioning, Friendster chose to scale their service by purchasing an SAN and using daisy-chained MySQL which resulted in considerable slave lag. For comparison, Facebook on the other hand used colleges to "portion" their database in the early stages of the company.
Instead of doing the rewrite, Friendster should have focused on trying to scale the service like Twitter did by bringing in PivotalLabs - if Friendster sharded their database for instance it would have helped them immensely and may have resulted in a different outcome for the company.
The way Coinbase is behaving is actually costing people money though, and if you look at the Bitcoin forums users have been pissed for months. They haven't just been having capacity issues letting people buy Bitcoins either; even once users have got Bitcoins into their account there's been problems with them delaying payments out, to the point other services have been telling people not to pay from Coinbase: http://blog.bitpay.com/2013/03/applying-late-transactions-to...
The combination of this being a financial institution, there being more robust competition, and the absence of lock-in might make this an exeption. I hate to be critical like this, but there have been months of user complaints and nothing but upbeat rhetoric in response.
Granted if Coinbase builds a solid product, this will all be dust on the road. The competition is not "good enough" yet.
