I've upload to Connect from my 60CSX using Communicator for a long time. Up until a few weeks ago the "Upload all new activity" feature worked, making it very easy. That feature no longer works, but there is a workaround: Set the device to ALSO record all activity to the microSD card, then use the Manual upload to upload the activities one by one directly from the card.
I've been complaining to Customer support to get the "Upload all new activity" feature working again. They are saying their hands are tied because the device is no longer on the Connect list of supported devices. They suggested I submit my request for restoration as an "Idea" at http://www8.garmin.com/contactUs/ideas/. I have done so and would appreciate it if all other 60CSx users would do the same. This is a suggestion from Customer Support.