I have created a test gallery using the same version of Juicebox as yourself (Juicebox-Pro v1.4.2) and exactly the same configuration options that you use in your own gallery but I have been unable to replicate the problem you are experiencing.
I do not know if it will help but I notice that your gallery's XML file includes largeImageURL entries but the corresponding images do not exist on your web server.
Try either uploading the 'images/large' folder to your web server or remove the largeImageURL entries from your gallery's XML file (either manually in a plain text editor or by editing your gallery in JuiceboxBuilder-Pro and deselecting the 'Large Images' checkbox before resaving your gallery). If Juicebox cannot find images that are specified, it may cause problems.
Also, in your email you say "I have been experiencing problems viewing JuiceboxPro galleries on both an iPad and iPhone where they previously worked fine."
If your galleries were previous working OK but now do not and you have not changed anything yourself, then perhaps something has changed on your web server (maybe a configuration setting of some kind or an entry in your .htaccess file) which may be contributing to the problem. Please check with your web host to see if they have made any changes recently which would affect your hosting account.
Also, to try to determine whether or not a combination of configuration options is the cause of the problem, try creating a basic Juicebox-Pro gallery with JuiceboxBuilder-Pro using only default settings and upload that you your web server to see if this works OK.
Hopefully this will point you in the right direction as to what might be causing the problem.