My Synology DS414 on occasion would go offline, and the only error I see in the log file (via Log Center -> Log Search) is "Error / System / System failed to get External IP." I.e.:
The fix that works for me is to hard code the DNS server (via Control Panel -> Network -> General). I use OpenDNS's server (208.67.222.222), but Google's probably would work as well (8.8.8.8). I.e.: