I've also had a lot of problems trying to change flights on co.com -- works occasionally, but mostly not.
One question: Say you book a deep-discount fare on co.com. You then call the elite line to change it later, and rebook to the same fare class on another day. Do you get 50% or 100% EQMs?
If you use the elite line and they actually complete a booking for a deep-discount bucket then the reservation will lose its onlineliness. If you use the co.com helpdesk it should remain an "online" reservation.