It wasn't just Waters who was gone at that point. Rick Wright wasn't a band member anymore either by that time and he only made some minor guest appearances on A Momentary Lapse of Reason. The only original member at that time was Nick Mason, and even he didn't contribute all that much.

If a band stops being the same band after a change in lineup, then what about bands like King Crimson, P-Funk, Jethro Tull, Deep Purple and Fairport Convention who have changed their lineups an absurd amount of times throughout their existence?

they have managed to evolve and be interesting and most of the different rests on one man

Crims - Robert Fripp, P-Funk - Clinton, Jethro Tull - Anderson, Deep Purple - Glover, I guess and Fairport - Thompson

not when the band is mostly a collective like Floyd or Who or Manics

I agree with Howard. Robert Fripp is the keeper of the Crimson flame and he alone determines whether the band he is currently working with has embodied the spirit of Crimson, regardless of personnel. It's kind of a unique concept, but then, Robert Fripp is kind of a unique guy.

I'm not sure the same is true of bands like Tull. Ian Anderson is the guiding light, but really, once they made their initial change, they've stayed pretty constant as a band over the years. And Deep Purple, well, like most metal bands, they just don't seem to trouble themselves about personnel changes that much.

Zepplin could have gone on if they really wanted to.
No band could go on with the loss of their lead guy like Nirvana.
I say that knowing that Little Feat is touring (never seen them etherway).
There are lots of older bands touring with one or two original members.
The main thing is the singer (though there are exceptions). But good bands have a sound and at some point replacements make too much of a difference.

I would say that a band is nolong a band when the there is only one original member of the band in it i.e. (Jethro Tull).

Some cases, it will be a band adding on a "Featuring" credit to the name. This happened quite a few times when one takes a major nosedive in popularity, or when it seriously loses focus.

A recent listen to Metamorphosis by Iron Butterfly featuring Pinera and Rhino (yes, that was how they were billed as) is clearly a case of the later. While the Butterfly were still a big name band by 1970, Doug Ingle changed the membership to include guitarists Mike Pinera and Al Rhino, with Pinera sharing some of the lead vocals. An attempt at getting a more Hard Rock sound, steering things away from the days of "In a Gadda Da Vida," it worked in some places ("Stone Believer," "Easy Rider") while not in many others. The final epic, "Butterfly Blue" was more of a showcase for Pinera and his talking guitar box, possibly one of the first albums to feature it. I'm sure some 60's Butterfly fans were gettihg worried that they were losiong touch. Ingle, Drummer Ron Bushey, and Bassist Lee Dorman were all there, plus some good production by Richard Podolor (who's Psychedelic mark was made on the effective "Slower Than Guns"), and it was a change, but it felt forced. Dorman, I thnk, was the one who kept the band running through The Mid 70's on, but after a couple of attempts to bring it back to life with fresh material, it still was not really the same.

Ingle, the main focus of the Butterfly sound, would leave the band shortly after the 1970 album.

Usually, this trait hits when there was nothing left to lose, but this was when a band was still running good until the album was released.

(Trivia: Oddly enough, a film featuring the In a Gadda line up, Musical Mutiny, was playing Drive Ins and Grindhouses by the time of the album's release)

Actually, it is a very complicated question and I don't think that it has a correct answer. A band can continue being great even if it looks impossible (like when Kurt Cobain died, if a guy like Eddie Vedder or I don't know who joined the band and started writing great stuff, the band could continue recording and calling itself Nirvana), and a band can be destroyed even if everything looks perfect (Guns N' Roses are a good example of that, because for them everything happened just because of themselves). On the other hand, I don't think that age is a factor, because as long as the guys have the attitude, they are a rock band (everybody knows what The Rolling Stones are all about)

What about bands with no original members left i.e. Napalm Death and Opeth?

Well, I don't know about Opeth, but Napalm Death today have absolutely nothing to do with the original Napalm Death. They WERE a hardcore punk band with metal influences, now they are a pretty straight up death metal band, so I think that what was originally Napalm Death is "no longer a band", and now you've just got a group that happens to share the same name and history.