It sounds like something in between the GXP-2000 and the Asterisk box… Could this be network collisions?
GXP-2000 phones have a switch inside them that basically let’s them “share” a single network connection with a PC. Are they trying to do this?
I don’t reccomend doing it. UDP and TCP traffic don’t play well together. the fact that it starts and then stops makes it seem like this might be the case, and that the interrupting traffic might be something like an email client checking for new mail. (But in the process, hogging all the bandwidth and messing up the audio path.)
UDP as a real time protocol really needs all the bandwidth to itself. The Asterisk box should have a gigabit network connection, and the talk path for the audio should have it’s own switched port on the network.
Don’t forget to check the bandwidth of the switch itself. If the backbone of the switch can’t handle the RTP traffic, you’re sure to have problems.