This is probably due to a change in version 0.5.0 of the migration plugin that disables the button after it is clicked once, to avoid multiple clicks having unexpected effects.
In our testing this change worked fine, but it seems like there was an issue for you.
I’m still not sure why this happened, but we will back out this change.
@james I can confirm this is working for me, I create a new site last night in local by flywheel and I was having this issue. The site had no plugins at all so it seems the situation is sorted.