internet drop-out

My internet randomly drops out, as well as the phone line.  Resetting the modem power does nothing...however I found that by disconnecting and reconnecting the cable to the modem, brings the internet and phone line back up. This is not a one time event. I have done that well over a dozen times!  At least 5 techies have been out here.  They changed the modem, ran new RG11 from the backyard pedestal to the interface and a new unbroken RG6 line from the interface directly to the modem.  Of course when they're here everything is fine. I did think, naively, that with the info I gave them, and what I did and they did, might just help them come to some reasonable conclusion. I'm not about to go into all the technical stuff since I pay them for that. By the way, I have a brand new Netgear AC1750 dual band router although the problem started before that purchase. Any ideas??

Thanks,

Ron