Not sure if this has been fixed recently or not.
In the "tag browser in Designer, if you move tags from one folder to another, the history values for the tags do not remain linked to the tag. It looks like the tag history vanishes, but I am told that it could be re-linked to the tags.
When tags are moved in the "tag browser" tool, the default behavior should be to keep the "tag history values" linked to the tags.