If the network map goes offline nodes can communicate offline as well, but new nodes cannot join the network until the map goes online again. Also, there can be many notaries on the network, these notaries can ether be a single node or the cluster of nodes.
If single notary goes offline but it is a part of a cluster then there is no problem, but if a notary is not a part of the cluster and goes offline then states assigned to that notary cannot be spent until that notary comes back online.
With these variations in the network map design, for availability reasons, the network map will no longer be a node. Instead, it will be a set of node info files distributed by a highly available service.