It sounds like you might be referring to adding image to a gallery in JuiceboxBuilder-Pro (rather than actually uploading your images to your web server).

Unfortunately, JuiceboxBuilder-Pro can handle images of no more than 4095px x 4095px when creating a gallery. (This is true of all versions of JuiceboxBuilder-Pro, including the current version, v1.5.1.) This is a limitation of Adobe AIR (the platform on which JuiceboxBuilder-Pro runs). Adobe AIR uses Adobe Flash Player as its runtime environment and the largest image size which Adobe Flash Player can handle is 16,777,215 pixels. This equates to a square image of 4095 x 4095. Please see this web page for details.

If you have images larger than this maximum resolution, then you could perhaps do one of the following:

(1) You could resize your images first in an imaging program (such as Adobe Photoshop) before feeding them to JuiceboxBuilder-Pro. (If you do resize your images prior to using JuiceboxBuilder-Pro, be sure to deselect the 'Resize Images' checkbox on the 'Images' tab to ensure that JuiceboxBuilder-Pro does not resize your images again.)

(2) There are plugins available to create Juicebox-Pro galleries with other programs (such as Adobe Lightroom) which do not have the upper resolution limit of JuiceboxBuilder-Pro. You can find details of these plugins here.
If you have Lightroom, Photoshop or jAlbum, you might like to try creating your galleries with these programs as an alternative to JuiceboxBuilder-Pro.

You should certainly be able to add small images to a gallery, though.
As a test, I've just tried images of filesizes 16KB and 28KB and both images display in the gallery as expected.

If the problem is with uploading your images to your web server, then the problem likely lies somewhere between your FTP program and your web server and your web host should be able to help you further.

I hope these notes help to clarify things.

However, if you continue to experience difficulties, please try to describe your problem in greater detail (let me know exactly what you are doing when the problem occurs and what, if any, error messages are displayed) and, if possible, please upload some of the images you are having trouble with (zip them, upload them somewhere and provide a download link) so that I can try to replicate your problem and help further.
Also, if the problem is with JuiceboxBuilder-Pro, it might help to know what resize dimensions you are using so please let me know this too.
Thank you.

Thank you for the additional information.

The only thing I know of that would cause the problem you describe (a broken image icon on JuiceboxBuilder-Pro's 'Images' tab) is if an image filename contain a comma (',').

The developers are aware of this issue and a bug report has been logged so hopefully it will be addressed and fixed in a future version.
In the meantime, as an image filename forms part of a URL when uploaded to a web server, it would be wise to use only web-safe characters within image filenames. Please see section 2.3 of this document for details.

You should have no trouble (either in JuiceboxBuilder-Pro or on your web server) if your image filenames use only these web-safe characters.

I hope this helps to explain what you are seeing.