Two Digital Phone Lines - Loud Noise Followed By Disconnect Requiring Redial Or Reset Of Modem

I have two digital voice lines (VOIP). Over the past two months both lines are dropping calls and this is happening progressively more frequently. I suspect that I have a gateway that is starting to fail.

Symptoms: Either one or both lines may be in use, it doesn't seem to matter. The line/conversation will be fine for any variety of time (long or short) then without warning a very loud 'static burst' sound is heard on both sides of the conversation and the line is disconnected. If both lines are in use, both will hear the loud noise and both lines are disconnected simultaneously. I can redial immediately and be reconnected, but the likelihood of being disconnected again seems higher when immediately re-dialing. The likelihood seems to be lower if the residential gateway is reset (by using the reset button on the back) before redialing. My wife and I both work from home and spend a great deal of time on conference calls. This issue is annoying for both us and our colleagues. Tech support simply tells me that they cannot see an issue with the modem and want to reset it. They don't want to replace a modem that 'appears' to them to be functioning. 

Configuration:  I have a fiber pair going directly to the gateway (not DSL or coaxial cable). The gateway modem model is BGW210.