Speaking as someone who in the past did support for DSL I think I can shed a little light on this....
DSL is a total mess... It works great when your close, but if you push for a high throughput there is so much that can go wrong. There are issues with distance from the head end switching station for DSL signal, quality of the copper lines that you run off of, even the moisture affects how DSL works due to the copper systems being so old the shielding isn't great and allows moisture in and causes noise.
It's just a mess and honestly you would be better off if you could use coax cable, or fiber. I realize that's not an option in all cases, so here's a few things to try.
Plug a standard analog phone into where the DSL modem is being connected to and press a button... Any button will do. Do you hear static? Speak into the phone and see if you hear echoing or anything other than just a clear dead silence line.
With that done, check that you are not running the phone line through a surge protector phone jack. They have caused so many issues for me in the past.
Then while this is extreme lengths to test, but I would unplug any phone in the house on that line and test it and then one by one plug a device back in and test and repeat until you know what is causing the instability in the signal.
I hope that this helps some, but DSL tech is flawed and unfortunately companies have pushed things beyond it's physical distance limits. Generally once you hit 1km of distance between your modem and the switching station things start to really get wonky. Not to mention that no matter the package you purchase speeds decrease the further you go. Keep in mind it's not the distance to drive or anything, but the distance of copper phone line your signal travels over.