Ahh, I fiddled a bit more and was able to replicate the bug you are seeing – I’ll create an issue so our devs can prioritize a time to work on the fix. Basically, it looks like the Live Link configuration settings are being copied over when the site is cloned.
As a workaround, you can go to the original site and disable the live link. From there, navigate to the cloned site and you should be able to enable the link without any problems.
Now that we have this fancy new “Bug” category, I’ve moved this topic here so that others can up-vote this bug and subscribe to it in order to follow along with any updates!