Interesting I had the same issue you were describing. I would have to reset the my ActionTech router once daily to restore services. I think you were in the right area with the number of connections. By chance were you running a Bit Torrent client? If so the number of concurrent connections used by the software will cause the connection table to fill up. What I did was limit the number of connections.
I have the same issues as noted in this blog and I am fairly certain that my NAS is a contributing factor. My internet access drops everyday and I merely reset the router to get internet access again. I've had this issue for only the past 7 months, since I installed our NAS. I have shut the NAS off for in upwards of a week, and I've never lost internet access during that time.
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