No, usually this is not normal. This could be indication of:
- Problems with the copper
- Your modem is dying
- Provider's port on DSLAM is dying
First case is when somebody runs electrically-fat tools like drills, punches and so on, increasing spikes in the mains. Modem could be unable to sustain the connection under this condition. The solution could be to provide better electricity to modem (use good UPS), to replace modem etc.
You could encounter the second case when there is rainy weather, so poorly isolated connections somewhere get wet and electrical properties of the copper line degrade. If this is the case you have to call to your line provider to fix the line.
To test this you could see diagnostic information from modem, at least upstream and downstream speed it negotiated. Good if your physical speed at least matches your tariff profile (it is unfair if you have downstream only 3 mbps, while paying for 10 mbps). Upstream in ADSL never could be more that 1 mbps (or more than 2 mbps if AnnexM is used), good values start from 800 kbps (other DSLs have other limits).
Best if you could view a DSL tone table. That is a table with 256 or 512 entries of hex digits from 0 to f, it shows, which tones DSL uses and how. Each letter represent a tone (frequency subband), in ADSL first ones are "upstream", latter - "downstream"; other DSL standards have other setups. Digits mean "how hard this particular tone is used", for example, if the line is very noisy or at this particular frequency band, or if that frequency is filtered out somehow, there will be a small use (0-4). The good condition is, as you probably think, is to have many large values :) By the way, upstream and downstream speed is calculated as sum of all tones in that direction (multiplied by 4k, if I remember correctly).
The worst thing here is, you have to figure out by yourself how to get this information from your modem. They all have significantly different interfaces and I didn't get used to work with this for 5+ years, so don't know much about current hardware, hard to help you here.
Third (and first) problem is easily tested by using another modem.
And fourth, well, the hardest to find out and solve, because to check this you have to get your service provider to cross you to other DSLAM port, better even to other line card.