Total speculation, but is there perhaps a rogue DHCP server somewhere on the network? In most cases there should only be one. If somewhere, somehow, a rogue DHCP server gets on to the network, it's possible that when a client's lease expires, it may get erroneously serviced by that DHCP server and end up misconfigured. Of course, if your lease times are greater than the length of time it take before being disconnected, that’s probably not the issue.
Again, just a complete shot in the dark. It could be lots of others things as well, but that's at least one thing I always look for when computers all over the place are suddenly becoming disconnected from the network.
P.S. It probably wouldn’t be a bad idea to record the TCP/IP configuration when a computer is first started and operating normally, then when it fails, check the TCP/IP configuration again and compare. Using “ipconfig /all”, see if you can detect any oddities, such as a loss of the default gateway, or a subnet change, etc.