Are cordons left untouched?

New grape owner here. My vines are trained on a wire for a year and are entering their 3rd spring. First year I let them grow wild, 2nd season I pruned and trained them to wire. Now going into the 3rd growing season.

My question is, do the cordons go untouched season after season? I only prune the shoots and canes correct?

There are lots of different ways of training grape vines so it depends on what you are aiming at. I just prune mine in winter to a central cordon, and in summer take the shoots off a few leaves beyond the flowers to stop it taking over the world. I gather you can train in a new leader every year and it might be more productive that way, but the way I do it is simple and seems to work.

So I guess I’m asking, once the cordons are established do I leave them alone every season and let them keep growing to get thicker and stronger? Or do I cut them and make new cordons every season?

It depends on your plan.  Making full use of available space or limiting next years potential growth to limited space.  With the varieties, climate, soil and space I have some vines are 100 feet long. Productivity seems to be dependent on access to sun more than anything else.  My largest old vine is now shaded  by a large tree at its roots and produces nothing there but at the end produces abundantly when after harvest the fruited branch is pruned back to one or two buds.