It was a number of years ago but I paid special attention to my modem settings. In there, and I can't tell you where because I've forgotten, there is a way to see the line stats for each line. They were labeled line 0 and line 1. I could watch the stats on line 0 drop in real time until is lost connection and have to restart the modem. If you can get the tech to help you get into the modem admin screens and show you were on there you can view the line stats it may help you convince them to do a more in depth bit of troubleshooting.