I've had a closer look at this via Safari's Web Inspector tool via the iPad to my laptop Safari client.
As I'm clicking on elements, in the Safari Web Inspector, they are highlighted on the iPad. Sometimes, that highlighting causes the page to display properly.
Other times, just scrolling up and down seems to bring the display back.
Elements that are hidden are still there. e.g. the search box. You can still click on the search box even though you can't see it and then the search drop down appears properly.
My conclusion is, the CSS and HTML must be loading correctly and I certainly can't see any obvious issues. Via the various web inspector tools, I cannot see any events or network activity being triggered when the display starts working.
I haven't looked at it in great detail, but right now there's nothing obvious causing it.
On my iPad mini XenForo displays and works fine; I haven't encountered any issues. This may be a browser issue WRT RTL. When I visit your site on my mini in landscape mode I get the same display as you do, if I rotate to portrait mode and back your site looks and works fine.
i used to have a problem similar to this from the laptop too ,
i think jack said once it is from java not loaded in the right way.
this sort of problems used to sort them self by them self
it stay for some times ( up to two days ) then get it self sort out
i never figured it out and it had not happen again for long time now without me doing anything !