When your dsl modem keeps disconnecting from the internet it's usually due to a bad connection somewhere between your NID telephone box and your phone jack.
Try taking your modem out to your NID telephone box, open the box and you should see a phone jack inside it.
Unplug the wire going into the phone jack and plug your modems telephone cable into the jack.
If it works fine then the problem lies in your telephone wiring or in your telephone jack inside your house.
Replacing the wire is pretty easy but you can have an electrician rewire it if you're unsure how to rewire the telephone line for your dsl.
If your dsl still disconnects after connecting directly to the NID box then you might have a problem somewhere in the main telephone lines in the ground or on the telephone poles.
In that case the telephone company will need to come out and repair the problem.