i have an old emac. using limewire pro.

so i start downloading some tunes. while this happens i return to the internet. about 10- 15 minutes later a little box pops up on limewire. Says it appears i do not have an internet connection.
to get it back, all i have to do is unplug- plug, not too hard. still it can be annoying. one of my friends said he thinks my isp shuts down when it thinks i am doing illegal or suspicuious downloads. i called tech at the isp and the guy said this can't happen, he's never heard of such a thing. any ideas?

thanks