This error message went crazy for several hours. I already found which column increased its length and updated the data table in the source, which now showed the correct length. But the error continued to appear. It turns out that this field was used in linking the fact to the size on the "Use Dimension" tab of the cube. And when you update the source, the binding created for this link is not updated. The fix is to delete (change the relationship type to "No relationship") and recreate this link.
Update . Since this answer still matters, I thought I'd add a screenshot showing the area where you might run into this problem. If for some reason you are using a string for Dimension-to-Fact relationships, this may depend on the increased size. And the solution is described above. This is in addition to the problem with the Key, Name, and Value columns in the Dimension attribute. 
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