I had this disconnecting problem too. Been having it for a couple of months, it came and went. I always complained a lot and the problem was fixed for a couple of days and then it started again.
Finally, I was fed up enough because I couldn't play Dota anymore due to the stupid disconnections, which happened after ever 30 seconds or a minute. I told them angrily that my phone had static and net is this blah blah blah and they sent a lineman the next day. He checked out the setup and came to a conclusion that my wire from the pole was damaged, had too many joints etc. At the time, he did a temporary fix, and gave me his number telling me to contact him if disconnection continues. Well the net worked for a few hours but then the problem started again. I called the lineman and he brought a new wire and changed the old one. I was surprised to see the bad shape of it, riddled with joints, wear and tear etc. Ever since the new wire, net has never disconnected, not even once and getting stable constant speeds.
TL;DR, the wire is the cause of disconnections majority of times since many houses have old phone wiring and never really bothered to change them when DSL started spreading here. So always check to see if your wire is old/damaged/has joints if you are having disconnections.
- - - Updated - - -
Well since the phone line buzzing is gone, your wire is not the issue. It could be a fault in the router or at their end. You have to call them and tell them your story about changing wire and stuff, then they'll give you a solution for it.