Well .. in the data folder there is a subfolder names "saved searches". It contains a bunch of .x1s files - one for each search in the navigation tree.
They are in fact .xml files, so you can open them in a text editor. Look for lines like this:
<Width>120</Width>
....
You can make a copy of those files before and after column widths are messed, if you do so, please let me know the result, so I can try to determine the cause.
Jogy
DISCLAIMER: Editing those files manually may break X1 UI. If you do so, make backup copies before that!