Maybe to help another answerer I'll ask this question for them. First, is the problem only occurring while in Rift, or does it occur elsewhere as well?
I had the same problem a while back. Turns out McAfee was causing the problem. McAfee would max out every processor core to 100% and the computer would pretty much freeze. Then 2-3 seconds later, it would all be fine again with no trace. If, by chance, this is the same problem you are having, then I would suggest just switching to a new anti-virus program considering they have had this problem for a long time now and haven't fixed it yet, to my knowledge.