Few things are more important in modern life than access to your money. That's why I would never use an online bank. I use a local credit union but "local" with actual branch offices you can walk into and talk to a human are the important thing.
The solution is the same solution as any financial risk: diversification. I have many accounts at many banks. If any one of them goes down, I’m fine. If multiple go down, I’m still fine in the interim.