I'll bet it's interferrence on the line. Probably somebody on the same line or sets of lines with a phone that isn't compatible. A while ago they stopped putting DSL splitters on the lines here, not sure if they still use them there or not (a splitter isloated the DSL and phone lines where they come into the house to prevent interferrence from each other), and I know that since they stopped using them, I've had a ton of problems.
I got a splitter off e-bay, and no more problems, though that won't help you there.
You should split it at the junction box and run a separate line to the modem from the splitter.