I have the same type of problem with my DIR-655. Some wireless devices, like my 2.4 GHz phone, can overpower the DIR-655 when the frequencies of transmission are too close to each other. I can often get around this by selecting a relatively unused channel on the router. This is likely what happened with your dropped connections. The router probably changed channels when you rebooted it. Try manually changing the channel on the router until you get one that doesn't drop the connection. One thing to remember about today's wireless devices is that most auto-seek the best (clearest) channel. Just when you think you've got the DIR-655 working, your cordless phone will seek a better channel due to interference and the phone signal overpowers your router's signal. The other day I lost both connections to my wired and wireless connections because I used a cordless phone while I was on my computer which just happens to be adjacent to the DIR-655 router. You can also try putting as much distance between the two competing devices as possible. This is the best solution, although not always practical.
Curiously, I had upgraded my router to a DIR-655 from a DI-634M router. When I turned off the radio (wireless connections) on my DI-634m, and used only wired connections, I still lost wired connectivity when my 2.6GHz cordless phone was used near the router.
Welcome to the wonderful world of wireless communication.

Today's digital devices (digital cordless phones) are marvels of technology.