If you're trying to run a copy task for your Theme(s) and the copy task appears to have gotten stuck, it could potentially be because your destination store has exceeded the maximum number of Themes it's allowed to have.
How to work around this:
1. No matter what, whenever you think you've run into a problem in Replay, we always first recommend contacting us at email@example.com so our Dev team can investigate.
It may be tempting, but if it's a possibility, try not to stop or touch the stuck copy task; it'll help our Dev team better look into things if we can see the data currently being affected.
2. Go into your destination store's admin, to Themes, and then count how many Themes you have under the More Themes section. Shopify imposes a limit of 20 Themes per store.
3. If you're already at 20 Themes in your destination store, you'll need to delete some of the Themes there in order to make room for the ones that Replay is trying to copy over.
4. Let us know. The stuck copy task can then be stopped/cleared, and you can try running it again. :)