Endurance Bosses (Timer) in MGS3: The chase sequence with the Shagohod. You had to dodge the bullets and get away. It is however also broken down in cutscenes as well.

Endurance Bosses (Puzzle) in MGS3: The almost-dead sequence is an endurance boss if you want the Shadow camoflague, but also a puzzle. You have to “die” and then use the revival pill in order to continue the game (an idea that I thought was a quite clever thought up puzzle).
The bosses that you fight during the game you can finish off in a “non-lethal” way by draining their stamina. It requires a great set of skill or some clever thinking to do this. If you do the game rewards by giving you special items (like useful weapons and camoflauge).

Recent “timer” example is the boss fight between Raiden and Fortune (who has some magnetic device that repels bullets which makes her impossible to kill) in Konami’s Metal Gear Solid 2.
The “puzzle” example would be the final chase sequence of the LucasArt’s game Full Throttle.

A mix between both endurance and standard type of boss is something you’d encounter in Final Fantasy 7. I.e. the fight against the Turks Reno and Rude. When their health was low enough, they would deliver some lines and run away. Similar was with aquiring Yuffie.
Another mix would be that from the beginning, the boss is impossible or hard to bring down. Which is more of a puzzle boss fight. Example is the fight at the colloseum in Prince of Persia: The Two Thrones. You had to make speed kill moves in order to blind your giant opponent before you can actually fight him.

I’m pretty sure I did encounter some more of endurance bosses in older games but they are clearly less common than the standard type. Where boss fights were common that they had to break the variation in some way.

Boss fights is since recently not a common game design element. Why, I don’t know, but they do tend to become a test of your skill. I could say that from a usability standpoint, boss fight segments are not very “user friendly” as those were more difficult than normal gameplay. Which would probably warrant for not including them in the game nowadays. Even less endurance bosses because the player would probably not understand what to do in that situation from the beginning.

I wonder if anyone has pondered upon endurance type bosses.

But then again, I actually don’t like bosses in games, it’s a too predictable trick.
(Still waiting for the SotC bosses, which may be interesting as it seems they are more like mini puzzle games than bosses – but isn’t any boss a kind of puzzle game?)

Any examples of interesting bosses?

I partially understand the trials and pitfalls of development having been involved with a 6 month student development project but it’s hard to believe that we keep seeing these boss models over and over again. And they wonder why game sales are slowing (somewhat).

Saw it in the Hulk recently, but I’m sure I’ve seen the same convention elsewhere.