More info: I now have the switch that's connected to the router syslogging me when its links are up or down, and it's telling me when the 1 Gbps link went down on the router. So I went looking for any log lines from the DSR-500N, and guess what: nothing.
If you're interested, these are the logged lines leading up to the reboot:
Feb 11 14:20:51 192.168.1.1 Feb 11 22:20:55 DSR-500N IPS [Local1-UTM] *ALERT*[1:1365:5] WEB-ATTACKS rm command attempt [Classification: Web Application Attack] [Priority: 1]: {TCP} xxx:xxx -> xxx:xxx
Feb 11 14:20:57 192.168.1.1 Feb 11 22:21:00 DSR-500N IPS [Local1-UTM] *ALERT*[1:2517:13] IMAP PCT Client_Hello overflow attempt [Classification: Attempted Administrator Privilege Gain] [Priority: 1]: {TCP} xxx:xxx -> xxx:xxx
Feb 11 14:21:25 192.168.1.3 Feb 11 14:21:25 2011:LinkStatus-6:port 1 link down
To clarify: these dramatic alerts happen all the time, hundreds per hour, I think it's nothing too concerning since we have tens of clients logged in to the same imap server all day. As for the "web-attacks" rule, I don't know what it means, D-Link doesn't specify these rules anywhere. Not very helpful.