Usually the most common reasons for a sessions failure is either your PHP session cookie expired from inactivity -- which seems unlikely here; or your IP address or some other key bit of information that makes your session unique was changed.
Since it looks like you're on a iPad via wireless, are you having wireless dropouts too that might result in the router re-assigning it a new number? Are you switching between wireless networks between when it works and when it stops?
If none of the above applied and you weren't locked into Apples "our way or bugger off" I'd be suggesting trying another browser. Sadly Safari is aging like milk right now; to the point many web developers have taken to calling it "the new IE" ever since Google absconded with all the talent.
See, originally Safari and Chrome used the same rendering engine, "webkit". Google didn't like all the "apple specific" bloat and they forked it, but in the process all the people who actually know how to improve it went with Google and gave Apple the finger. (it was NOT a clean separation).
Because of that we're going to be seeing more and more iOS and OSX issues with Safari much akin to the HELL that was IE6 from 2003 until quite recently... this may or may not be one of those cases as well.
Apple's "It just works" is starting to ring hollow. :(
-- edit -- this is unlikely on a iPad, but if you are using any sort of proxy or worse, realtime re-assigning anonymity proxy like Tor, that can also trigger said behavior. Another obscure possibility is an infection... you know that "apple's don't get virus'" thing? Yeah, not so much, PARTICULARLY on iOS.
http://www.macrumors.com/2015/09/20/xcodeghost-chinese-malware-faq/Admittedly NOT really Apple's fault, though partly theirs as the "ease of access" to the xCode development suite is hampered by a lack of trustworthy and fast download sources... but really it's developers downloading it from non offical sources that opened up this can of worms. I've heard RUMORS but nothing concrete about it doing things like messing with sessions. It's unlikely this is the cause of your problem, but it's also not outside the realm of possibility.
