Here's what I think is happening: DHCP clients attempt to renew the lease about halfway through the life of the lease. A DHCPREQUEST to renew goes to the DHCP server that granted the lease, and if the lease is extended, the lease expiration time is adjusted to reflect this. There is no
ipconfig /release, which drops the assigned IP address, involved, so there is no interruption in connectivity. If, after some interval, the DHCP server which granted the lease cannot be contacted, DHCPREQUESTs are sent with no server specified, and if no response is received before the lease period ends, the lease expires. At lease expiration, an
ipconfig /release occurs, dropping the assigned IP and interrupting connectivity. A broadcast DHCPDISCOVER request is made for any listening DHCP server, and when a server responds, a new lease is requested (
ipconfig /renew does this if no lease is active). When a new lease is granted, connectivity is restored.
I think your problematic machine for some reason can't reach the assigning DHCP server, and so cannot receive a renewal. At lease expiration, connectivity drops, and a broadcast DHCPDISCOVER request is issued. The DHCP server hears this, responds, and a new lease is negotiated. Lather, rinse, repeat.
I predict that the connectivity interruption changed in sync with your changing the lease interval. If it did not, my theory is wrong, and you can stop reading.
If the loss of connectivity event happens at the end of a lease interval, we've got to figure out why the DHCPREQUEST renewal is not getting to the DHCP server. One possibility is something wrong with the routing table on that machine. Use
route print when the machine is connected, and
ipconfig /all to show the lease details.