There are a number of reasons that can present problems like this.
Usually its noise on the line, this can be present in a number of ways.
1) Pick up the phone - check for static noise on the line
2) Does your modem drop the connection when a phone call is made.
One of the common problems is poor filters on the line - this is the little box that you plug your adsl modem into along with your actual phone. If either of the above are being experienced try changing your filter as cheap ones of these can be problematic (and they do fail).
If you dont get the above ring your telco back and demand an engineer come out. It is not unlikely that when an engineer has been working on cabling to another premises they have disturbed your cabling in the street cabinet and your contacts are not great.
It may be worth changing the filter if access to your telco is not easy as its an easy and cheap way to prove its not your problem. Ideally you want to be able to show any engineer that comes the exact problem so they can realise there is an issue to be dealt with - so if you can find a way of reproducing the drop out all the better.