Is it possible to repair a corrupted custom toolbox?

Answer

There are no tools in ArcGIS Desktop that support or repair corrupted custom toolboxes.

The best solution is to recreate the desired toolbox. Refer to ArcMap: Creating a toolbox for more information.

Note:
To prevent future data loss, if the event a toolbox is corrupted, make a copy of the original working toolbox that serves as a backup. Refer to ArcMap: Copying toolboxes for more information.