You have described my situation 1 year ago. Verizon replaced the line from pole to NID, ran a direct line from NID to modem jack (then I was able to eliminate all filter on my ancient phone. Cable from modem to jack was also repaced. Then thanks to the experts here I figured out I was about 2.5 mile from the Central Office and since some of the copper wiring could be as old as 20+ year the issue was not going away. Before switching I would contact customer service and see if they will upgrade you to FIOS, That is what they did for me and my speeds are up to 6 times faster on download (.75 Mb/s - DSL 5.0 Mb/s - FIOS) . There was no extra charges (install, router etc) at all, and my monthly payment is still under $35.00 for conventional phone and FIOS
Take a quick look here before you leap http://forums.comcast.com/t5/Home-Networking-and-Router-Help/bd-p/10
You are not the only one. This is happening to people all over the country. Verizon seems unable or unwilling to fix the DSL issues. Check the forums here and you'll see many other posts similar to yours. Now multiply that by thousands, since most would never come here to post about their problems.
I have the same issue. I loose internet connection while DSL link stays up. the only way to reconnect the internet is to power cycle the modem, disconnecting and reconnecting the phone line from modem does not fix the internet connection. contacted Verizon and was told i need a new modem cuz my modem has gone bad. I work in the industry and have access to best modem the industry has to offer and want to use one of them but Verizon would not give me the configuration info and insist that i buy one of the cheap modems from Verizon. how is that for boxing the subscriber in?