Makes me think there is something else going on. These routers work well out of box unless something is effecting the connection between it and the modem.
I would try a different model router, I recommend a DIR-825, 655 or 657. These are solid routers and I have tested these.
One thing I would do if you can, take the router to a different location, family, friend or nieghbors place with internet and see if this problem is tracking or not. I bet it might not. If not, it might be a compatibility issue with the modem. I've seen only a few issues with Cisco modems. More with Arris. I prefer Motorola SB 6 Series modems.
If anything, take it back and try a different model router.
Let us know how it goes.