I keep trying to add CNAME records. And, they get listed immediately after adding them (with no errors). But, when I go to a different page and come back, the changes are gone.
Also, I deleted an existing domain redirect, hoping the CNAME records would take effect. When I couldn't get them working, I tried adding a new redirect as a temporary fix. But, it just causes the domain to point to some generic green GoDaddy message page, "The domain ... is no longer parked by GoDaddy."
When you add something to the zone files, they do show up on the page, but there is another place to click to SAVE the changes you just added. Are you also doing that? If not, then the changes will disappear when you leave the page.