This can happen for a bunch of reasons:

- the computer serving the file doesn't have enough bandwidth or processing power to send the file at a steady rate
- Internet sluggishness, that is sometimes data travels very quickly but overloading occurs and then as the data needs to be sent again the rate drops. While similar services may be fine, it is possible that LimeWire traffic may be using a slower part of the network.
- your computer may be busy doing something else, but if you're just downloading (and only connected to an ultrapeer in some cases) then it shouldn't be a factor

I notice this problem as well although it varies depending on what host I am downloading from.