So, as far as I can tell, every DIR-825 has at least two problems:
1) Constantly restarts wireless access, manifested in logs as "2.4GHz Band: Wireless restart". Possibly this is based on receiving interference from other wireless devices, or heavy wireless usage. Each restart causes many connections to drop.
2) Randomly loses firewall/NAT state information and drops incoming and even outgoing packets. This occurs regardless of firewall settings and seems to be that the router forgets about particular connections and decides that further packets on that connection are invalid.
Neither of these problems has any solution - this "as good as it gets". There are also additional problems related to 1.11 firmware, and possibly other problems as well.