As far as I'm aware, Discover only starting banking very recently and thus was never in a position to be bailed out. Discover accounts are all FDIC insured, so there's no need to worry about it being safe--it will be. Also, if you're interested in alternative online savings accounts with higher APYs than traditional brick and mortar banks, American Express Savings
is another great option! I myself went with American Express over Discover because at the time I had an Amex card but no Discover card, so I decided to go with the company that I knew and trusted. I hope this helps you in your decision!