Yep, all sorts of weird stuff happens when Routerstats has been logging into the DSL-2640S for a while, the MAC address (WAN & LAN) tend to disappear from the router status page, DHCP/DNS stops responding (as you've seen), incoming pings get increasingly laggy and eventually attempts to log into the GUI fail altogether. Not long after all that, it just gives up and reboots. Maybe some kind of memory leak?