Well, remembering the widths of the columns worked already in the past and therefore I was astonished to read your post. But you are right, the column widths are not remembered anymore on exit, just loaded on startup from uedit32.ini and applied to the columns.
First version of UltraEdit supporting saving the column widths was v17.10. After some tests with various versions of UltraEdit which I have archived, I found out that remembering the current widths of the columns on exit works up to UE v126.96.36.1992. But saving current column widths stopped to work beginning with UE v188.8.131.522.
I have just reported this issue to IDM support by email and suggest you do the same to increase the priority for fixing this bug.
In the meantime you can open %appdata%\IDMComp\UltraEdit\uedit32.ini with Notepad while UltraEdit is not running and add or edit in section [Settings] the entry Explorer File List Columns= with the 4 pixel values separated by the vertical bar | between the values.
Explorer File List Columns=200|115|250|55
First value is for file name width. Second value is for column date modified. Third value determines the width of column file type. And the last value is for column with file size.