As someone who has worked with problems like that before, my first guess would be "Signal Level" coming into the house and to the Cable Modem.
Most routers will 'drop out' when the signal level drops to a specific LOW level.
Phone modems will do that too.
In my most extreme example the cable company had to replace both wires and amplifiers outside the home to fix the problem. They even replaced a splitter in the attic. But the entire problem was on the cable company, not the subscriber.
You need to get a Cable Company technician out there to check signal levels, etc.
And, stay on them till they get it fixed.
Good Luck Mate!
The Doctor
