As far as I can tell, the feature in the Master Data Manager website that lets you edit an entity and reposition the attributes simply doesn’t work, if the entity is sufficiently complex. It appears to move them randomly. When I come back later, they sometimes appear to be back where they started.

It does seem to work for entities that have only a few attributes. I haven’t been able to find anything about this issue so far. I will report it at some point, because it can make the Excel Add-in hard to use if you have very many attributes, and especially if they are related (e.g. street, city, state, and ZIP).