Please notice that I have used the word "kept" in the subject of this post. This means (at least in the case of my rebooting issue) that I have identified the problem and have a work-around. My solution is not ideal (although it works) and ideally this will most likely only be solved with new firmware but if anyone else has run into this and has a better solution, please let me know.
I had purchased the DIR-685 to replace an old DIR-655 that had seen much better days. I specifically got the DIR-685 because I liked the idea of the NAS built-in to an appliance that was always on as it is. So I also purchased an Hitachi Travelstar HD20500 500gb 2.5" SATA hard drive for the NAS option. My old DIR-655 was hooked up to a Siemens Speedstar 4100 DSL modem and I had the PPoE on the DIR-655 so I setup the new DIR-685 in the same manner. That all went without a hitch. I was able to access the Internet and connect to the router via wireless without any problems. I inserted the new hard drive, formatted it, setup access rights and ran an initial backup of data from my desktop to it all without any problems. Shortly after I finished all of this the rooter rebooted. I noticed upon rebooting that the data and time had been set back to 01/01/2000 12:00am. The router did successfully NNTP after re-establishing it's Internet connection and all other settings were still as I had set them. This started occurring anywhere from 2 to 4 times an hour. I immediately checked to see if I was running the latest firmware (I was) and that was when I found this forum. I searched this forum for similar problems (across their whole router line) and individually tried any other fix for router rebooting issues I could find. Those issues included the NNTP issue, turning of UnPNP on the router, cloning my pc's MAC address and turning off DNS relay. None of these solved my problem and once I determined that the fix suggested for each one of these issues did not do anything for me, I returned the routers settings that I had changed for that fix back to the way I had it set.
It was at this point that I realized that my backup software had successfully completed completed a back of my music files to the hard drive in the router. This is close to 120gb's of data which means that the router had gone for at least an hour without rebooting itself when this backup had occurred. I thought I might have a compatibility issue with the hard drive so I unmounted it to test my theory. With the hard drive unmounted from the router, the rebooting stopped. I let the router run for about 3 hours this way and then reinserted the hard drive. After about 15 or 20 minutes the router once again rebooted itself. This time I paid close attention to how much time went by before the router rebooted again and 15 minutes later the router once again rebooted itself. Since the router was not rebooting when there was a constant data stream going to the hard drive and also since I now realized that the rebooting was occurring every 15 minutes when data was not being written to the hard drive, everything pointed to the router powering down the hard drive after inactivity. That setting was still at the factory defaults which turned out to be 15 minutes. I changed that to "never" and the router has remained up and working flawlessly ever since (about 3 days now). I would prefer that the router spin down the hard drive after a period of time of inactivity but having it never spin down is a small price to pay to maintain an otherwise stable router. Hopefully this issue will be fixed in future firmware.
On a side note, I have read (on other sites) some peoples complaints that the router is too noisy when a hard drive is running in it. I think this may be more of an issue with the hard drive and not the router itself. The Hatachi drive I purchased is so quiet I have to put my ear up to the back of the router to hear it running. The internal fan in the router (which is a little loud) has only come on when the router is booting itself and has never been running otherwise. So in other words, the router is virtually silent with this Hatachi hard drive running in it.