I'm seeing something similar. My unit doesn't completely shut down, it just seems to forget to respond to its name. Even in DHCP, it still seems to maintain its lease.
But, I've given it a name, and then from my Windows boxes, I can ping that name and connect to it via the Web Interface. After a while, it just stops responding to that name, but I can still access it by its IP address.
So, some service seems to shut down after a while. DHCP seems like it works, since it maintains its address and entry in my router's DHCP list. But, I'm wondering if a NetBIOS service or something similar decides to take a break after a couple hours of work.