K-T Survivors That Died Out in the Eocene

I noticed a while ago that there were several larger taxa of vertebrates which survived the Great Dying at the end of the Cretaceous quite well, but then became extinct during the Eocene. Notably:
[li]the Champsosaurs, aquatic reptiles resembling crocodiles[/li][li]the Multituberculates, rodent-like mammals that were neither marsupial nor placental[/li][li]the Sebecosuchia, long-legged, narrow-headed land-living crocodilian carnivores[/li][/ul]

There were two or three other groups that caught my attention which I cannot remember at the moment.

Is there any obvious correlation behind why these groups survived and then died out? Was there a less drastic mass extinction in the Eocene?

Well, first off, multituberculates didn’t become extinct until the early Oligocene. It is thought that champsosaurs may have likewise persisted until the early Oligocene.

Having said that, there were a couple periods of extinction during the Eocene - the first about 37 mya, and the second about 33 mya. It is thought that global cooling was most likely responsible for these events. This gradual cooling trend continued well into the Miocene.

In the oceans, foraminiferans suffered heavy (but gradual) losses, as did bivalves, gastropods and echinoids. Warm water critters tended to suffer more than cold water ones, supporting the cooling hypothesis. On the land, those vertebrates who inhabited warmer climes likewise did worse than those in cooler climes, but the loss was not nearly as great as what happened to marine invertebrates. As such, the Eocene-Oligocene extinction is generally referred to as a marine extinction. I haven’t had much luck in finding actual numbers for terrestrial vertebrate losses, though.