My credentials were showing as disconnected, this is what eBay support suggested:
Please log out of all Shopify sessions and clear your browser history/cache. Here are instructions on how to do so depending which browser you are using:
Once you have done so, please restart your browser using either a Chrome Incognito window or a Private Firefox window.
Using this new window, please access the Sales Channel again and attempt to Refresh your eBay Credentials again.
I actually just logged into my shop from a different browser, did the refresh credentials thing, and that time it worked. So I didn't even have to follow the full browser cache steps suggested by eBay.