@Handmadebygracious Are you trying to do this using an Etsy app or via browser (it makes a difference as to possible causes and potential solutions, otherwise we have to guess).
I also have this issue. I've tried using Chrome and Firefox. After adding a variation and clicking Save & Continue, the buttons turns gray and nothing happens. No loading. It just stays there (I've waited a long time).
I've tried creating new listings and modifying current ones.
Someone please advise.
Well I spent 30 minutes fussing with this and as soon as I post- I figured out my mistake:
I forgot to add the 'Options' to the variation. An example for anyone else who has this issue: My shelves come in two and three tiered options. So I added the 'Tier' variation, but forgot to add the 'Two' and 'Three' options. The variation will not save unless you provide options- and you will not be given any errors or guidance in the window.