What are the MAC address settings in your grub file? Is it set to the same as the MAC of the NIC or a 'fake' one? Is it blank?
There might be an issue with DHCP renewal, as you say the box drops connection every couple of days, maybe look at the lease time if it is about the same.
I would try setting MAC to blank in grub and setting a DHCP reservation in the router (not static in DSM), see what happens, then also try setting MAC to match the NIC and test. You could also try a static address in DSM, but make it outside of the router dhcp scope.