If I was you, I'd politely point out when you next call NTL about this problem that you have previously called on numerous occaisions, and that the problem is still not resolved. Ask them to look at the calls logged against your account - they should be able to tally up the number of times you've had this problem. They should also be able to access logs for your modem to see exactly how many times the problem has been occuring (so probably not a good idea to exaggerate the problem, as they'll have access to the data).
If necessary, escalate this issue to the representative's manager, explaining all the problems you've had, and that although you're eager to get these issues resolved as quickly as possible with the help of NTL's 1st-line support staff, it seems that this may be beyond their capabilities, and that you'd like assurance from the manager that this will be escalated to any tier-2 or senior support staff.
Start logging the number of times you've had to call NTL about the same problem without it being resolved successfully. Also, take names of people that you speak to - this always helps ensure your call isn't ignored, as people don't like to know that they're personally responsible, so they're more likely to deal with your call.
When someone says to you that they need to go away and do something, or they need to escalate the issue to their superiors, make sure that you get a timescale of when they will get back to you and via what means, and explain to them that you will contact them personally if you don't hear from them - this also means people are less likely to put your issue at the end of their to-do list. Get their extension number, or some other means of contacting them personally... they'll most likely not want to give you this, but if you explain that you have already had to deal with numerous different people for the same issue, and that each time you speak to a new person you have to waste both your time and theirs going over the same details again and again and again, then you'll usually get something.
Finally, remain calm but be forceful with them. There's no point in shouting down the phone at them - firstly because the person you're shouting at is 1st line and maybe not in a position to resolve the issue personally, and secondly because you'll just p*ss them off so much that they'll give you some excuse to get you off the phone, and will then ignore your issue for as long as possible. You will get much better service if you remain calm and collected, but are also determined of what you want achieved and by when, then if you lost your temper. (ps - this technique is the same for restaurant waiters and air hostesses too!
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Finally - and I'd only use this as a last resort - if you're a long-term customer and you pay NTL a lot of money each month, then you might be able to get somewhere by speaking to their retentions department, and asking for details about cancellation procedures. Don't actually say that you want to cancel, just ask for details of the steps to follow... and then casually drop in to the conversation that you're having so many problems with your broadband that you're considering going with one of NTL's competitors. If you do this properly (and if you get lucky) you can get the person from retentions to put some pressure on the support team to prioritise your call.
If all the above fails, then there are some people here who might be able to lend a hand
