I've only had 1 sheep die on Popham, if you stock up on the medicine its ridiculously easy to make sure they dont die.
Here's a picture of a sick ram:
I will agree that there's no reason to play on Popham anymore since the main point is getting animals. Aside from leaving my town to get the fish bladders, There's no reason to do anything else since I'm almost positive the majority of the server is waiting for the ferry to let animals go to providence. The other group of players that actually play are the witches who are trying to end the server.
Aside from that, you're better off switching back to providence to do stuff because you'll actually be able to keep your progress on that server. The time spent on providence with a far better established town outdoes the slower progress on Popham with the incentive being the inheritance statue. Let alone any items your receive on Providence will actually be kept.
Overall, the idea for these servers that end are good, but after the initial rush of attaining whatever is being released is done, theres no point in playing past the point to keep the animals (or whatever will be released next) alive which results in a large amount of inactive players/bases that we have now in comparison to the first month.