OK, I've done what Tekwych suggested, and I also uninstalled/reinstalled Hero Lab, and reimported the portfolios. I have 17 characters, and a single character in each portfolio.
I have the latest v12.3 installed, all PF, plus the PF Basic Pack v3.14. Again, it's an iPad 2, running iOS 9, latest version of HL for iPad.
The character I'm trying to run is a mythic character for playing in Wrath of the Righteous. After a few minutes of the app being open, it crashes with no message. Whether I reinstantiate from the background, or dismiss it and restart it, it makes no difference; it still crashes out after a minute or two whether I am interacting with it or not (if I just load the character, and then leave it sat there, it still crashes out). If I've been using it in some way, to record changes in play, sometimes those changes are still there after it crashes, and sometimes they're not.
It looks as though other characters are fine, and don't crash out, so I'm thinking that this is an issue with either the mythic ruleset, or the PF Basic Pack (I'm using some options from that), or their interaction. Given that it crashes out without interaction, it sorta smacks of a memory leak perhaps, in one of those implementations.
Any further suggestions?