The network is connected enough so that there is multiple ways to route messages between each pair of nodes. If a node dies on a route between two nodes, messages are redirected across other routes that don't involve the dead node.
Very good, and the same applies to nodes that can't get an update within 15sec.
That really isn't good enough.
As I said, the block time needs to be more than several times the maximum end-to-end propagation delay. This is needed to prevent competing nodes from generating blocks at the same time and convincing large parts of the network that their respective block is the winning block. If competing nodes can convince large parts of the network that their respective block is the winning block, you risk fragmentation of the blockchain. Having the block time be at least several times the maximum end-to-end propagation delays helps prevent competing nodes from convincing large parts of the network that their respective block is the winning block.
So what is the maximum end-to-end propagation delay? Bitcoin networks are constructed by randomly connecting to IP addresses. This means that Bitcoin networks ignore geographic locations, so end-to-end communication can cross the globe multiple times. The network construction also does not limit the width of the network, so end-to-end communication can require numerous hops. Add processing delays on each node and you can easily get a maximum end-to-end propagation time that is tens of seconds.