I second that …
Particularly if you have long varchars you may choose not to show everything in each field in order to get room for all fields (or just the important fields) on the screen.
So I think there should be a setting “Keep user settings for column width's” alongside the existing setting “truncate column headers to max data size). It should work not only when sorting, but with all queries …
It's now without problems implementing that however – especially if it is a request that the setting should be saved when the application is closed. I'd prefer then, that the settings be stored in the MySQL database itself rather than an .ini file. However when connecting to a remote host (and you don't have a local installation of MySQL) you might not have privileges for that!