Bus runs in a straight line from one network device to another. So if one gets disconnect then the all the devices connected down the line get disconnect.
Star runs to a central device like a switch, so if the switch itself fails then the whole network will be disconnected.
Ring is like a bus except it connects back onto itself. So if one device fails they all fail. The exception is if there is a redundant inside ring like that used in FDDI (fiber ring) then if both get disconnect from one device then they all do.
Mesh is high redundancy. Only one device would be disconnected if all the connections were to fail for that device. You can have many connections to other devices thats why its less likely to fail. The only cause for failure at this point is really the power and if you just don't have any. Even if one of the connections between two devices fail there is no effect on network and they can still communicate through other channels.