When JuiceboxBuilder resizes a PNG file, it converts it to a JPG file and transparent regions are rendered as black in the main image but white in the thumbnail. The developers are aware of this inconsistency and it has been logged as a bug.
When choosing not to resize PNG images (by deselecting the 'Resize Images' checkbox on the 'Images') tab, the original PNG images are copied across to the gallery's 'images' folder (unprocessed) but with an incorrect '.jpg' file extension. This has also been logged as a bug.
To regain transparency, you'll need to rename the file extensions in the 'images' folder from '.jpg' to '.png' and also change the file extensions in the corresponding imageURL entries in the gallery's 'config.xml' file.
Please note that the thumbnails (in the 'thumbs' folder) will have been converted to JPG files (with transparent regions rendered as white). If you like, you can just use the imageURL paths (after correcting the file extensions) for the thumbURL entries by manually editing the 'config.xml' file. Juicebox will dynamically scale the images when the gallery is displayed and you'll have transparency in both the main images and thumbnails.
I realise that this is inconvenient and adds a few extra steps to your workflow but, until the bugs are fixed, it is at least still possible to display PNG files with transparency in a Juicebox gallery (with a bit of work).
Both of the PNG related issues above have been logged as bugs and should be fixed in a future version (but, unfortunately, I do not know exactly when this might be).