I have an account at UFBdirect (aka AXOS bank), they pull a sneaky. When they raise their interest rate, they create a new name for their savings account and DON'T change the rate on your existing account. At first I opened a new account and transferred my money from the old account, so I now have 3 savings accounts there. Direct, Elite, HighRate, and now Preferred.

But then I complained why they didn't just increase the existing accounts and they immediate replied that they'd upgrade the old accounts. Great. But a PITA, because you have to go to the main page before logging in to see if they have a new higher rate.
Monday I saw they went up from 4.21% to 4.55%, so I messaged and asked them to upgrade my accounts, which they promptly did. Today (Wednesday) I logged in to verify the upgrade, and WOWSA! the newest rate (which I got) is 5.02%.

I bet that when rates go down, they'll automatically lower it.

CIT just bumped up to 4.20%. Everybody else besides UFB just flat-out updates their rate.