G'day Zernik,
I agree with SJ, the NIC/Switch is a good place to look.
Try starting a continuous ping to the box and/or another device on the same switch to see if you get dropped or high latency packets at the same time as the breaks in the 20GB copy.

How are you accessing the data? NFS/iSCSI/CIFS?

I don't use 3Ware, but I assume they have a logging facility? Does it show anything odd?

Rgds Ben