Hi, this isn't restricted to just the iPhone, I'm getting the same problem on my Android mobile.
The blank space seems to be a missing slide image, and this image is coming back with a broken URL. The images are a tad large at 250KB, you could try making them smaller, but they should still load fine even if it takes a bit longer.
It looks like your theme is filtering the slideshow shortcode and adding paragraph tags around the slides, that can cause issues too.
The first thing I would do is deactivate any other plugins and test the slideshow to make sure there aren't any plugin conflict.
Then try compressing the images down to less that 150KB each. For taking care of the paragraph tags, you could try looking for the shortcode filter that is adding them, but the simplest way is to use the slideshow template tag in your theme instead and not add the slideshow in the post editor.