Actually, "bank" security doesn't get compromised as often as datacenter security. So, what you get is a breach that effects perhaps dozens of banks in 5 or 6 states. joy. So, yes you can generally recover your money, but different financial institutions will handle the issue differently. This happened a couple of years ago to some of the folks I work with, and most of the institutions replaced the stolen funds immediately. Some, however, took a few days to do it, and pissed off a lot of customers. Even if the funds are replaced immediately, there's still the cost and inconvenience of card replacement which also includes updates to automatic bill paying that uses the cards, and any other online commerce sites you use.
The situation isn't always very clear where responsibility lies either. Look at the Target breach: FireEye appears to have provided information to Target that perhaps should have caused an earlier response, but you could also consider the info a bit ambiguous, or perhaps the IT staff had a lot to do, and not enough eyes to watch everything. In any case, it's always easy to second guess.