Modem Problem?

My modem are having problems. From time to time the modem just power goes off and turns back on by itself, the Power light turns red, then turns green. I don't know the cause of this.
The power adapter isn't loose. This is my first time encountering this problem.
I'm currently using a ActionTec model GT704WG modem from verizon.

Frequent restarts consist of power failure.

First, replace the power supply. If that does not help, then replace the router.

But this only happens with I use the internet around 12am~7am. On other times the modem is working perfectly.

Must be down times by the Internet Service Provider. Call them and see what is going on with the modem around that time. That is more technical and outside of our expertise.

Down times?
The modem turns off then back on which is like maybe less then 1 minute.
Then it starts working again for a while, around an hour (haven't timed it).
If the internet has down times wouldn't just the Internet green light not be on and it won't be on for a while?