|Since the LAN works fine all the time, this points at a router, or provider issue.|
I recommend first checking for more recent firmware for the router. If there is newer apply it. If the issue stops, problem solved. If that doesn't fix the issue, try resetting the unit to factory defaults and reconfiguring it.
If neither fixes it, check with your provider and have them look into the modem. If it, and the ISP's network seems to be working ok, it might very well be time to replace the router. If possible, I'd recommend trying one for a week or so to see if the problem happens again. If it does, then it has to be the provider, regardless of what they say. If it doesn't, then you know it was/is the router.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.