What are the chances of creating a P2P network where a set of peers can get isolated from the rest. Obviously, I don't fully understand P2P, but I would think that you can get a small group of peers that only know about each other when the real main group of peers is somewhere else.
Connecting to a P2P network requires a bootstrap system which can be implemented two ways: i) with central peers (i.e., peers everyone knows about) or ii) by publishing seeds adresses on a know URL for example. This makes sure that all peers are connected transitively.
If method i) is used and all central peers are down, then there is a risk of isolation for sure, especially when alive connections between peers are closing over time.
If method ii) is used, seed addresses can be republished/updated on the URL. The weak link becomes the webserver serving the URL. If it goes down, risk of isolation increases just like in i), when connections are closing.