It may not be the router causing the problem at all, it may be something else connected to the router, but using it as a path.
More troubleshooting is needed.
I've seen these sorts of problems caused by all sorts of things, including: loose coax connectors nearby wireless devices allow in noise; wireless routers too close to modems which then overwhelms internal RF shielding; power outlets with hot/neutral reversed causing hot chassis to ground out through the coax, etc.--
If it's important, back it up... twice. Even 99.999% availability isn't enough sometimes.