Do you run any remote shutdown software ?
It could be also a virus that has spread into the network or a heatup issue . After reaching temp of about 46 C , your machine might shutdown automatically .

About the limited connectivity issue it is due to IP ( Internet Protocol ) Address Conflict issues . Is their a DHCP server that assigns IP to all the machines ? Try to assign static IPs to each machine using your router/hub , that shall solve the problem for good .