안녕히 계세요!
I have question about verb in phrase: 안녕히 계세요. Is this verb here 견디다?
But then imperative present informal high is 견디세요. So, what is the story behind 계세요?

Question

Answer

Nope, the base form of it is "있다", and "계시다" is the honorific form of "있다".
The ending "-(으)세요" is used to make a sentence into an imperative.

e.g.
계시다 + 세요 => 계세요.
드시다 + 세요 => 드세요.

However, "계세요" in "안녕히 계세요" is just a fixed expression when a guest leave like "안녕히 가세요", "어서오세요", etc.

\^o^/

Answer

The verb is 계시다...

Answer

Take a look here: http://en.wiktionary.org/wiki/%EA%B3%84%EC%8B%9C%EB%8B%A4