Well, Bitfinex is using Incapsula (https://www.incapsula.com/) which uses who-knows-what voodoo to detect suspicious connections. In this case it presents captcha and MyBitcoins gadget (obviously) fails the captcha test.
It's not due to number of requests - I've had it happen when gadget is set to poll Bitfinex once in 10 minutes, and their official API limit is 60 times per minute.
It makes no sense to have captcha protecting API endpoint, but that's how it goes with those CDNs that are optimized to work with websites instead of APIs... I've contacted Bitfinex support and reported this, I'll update here if it goes anywhere.