Hardware is lovely...
- except now phones are too big to use as a phone, so 5s will be my last unless the trend changes.
- Mac's still are lovely, except I can't stand glossy screens, so 17" 2.93ghz will be my last.
- IOS and OSX are just too demanding now. There was a time when you just pressed download and it worked. Not anymore, as a minimum you now you have to comb through settings and turn off everything that's defaulted to on.
As to this particular issue... If you haven't noticed background activity related to mail on your device, then maybe your router will give you indication of the activity going on. Anyway, on my device it's clearly apparent with frequent lock-ups. (I also saw a couple of other threads re' mail issues that seem to suffer from serious background activity issues).
I've given up on trying to figure out what is going on - like you I have a mix of IMAP & POP accounts. For me, IMAP seems unaffected. However POP was screwed up as soon as I installed IOS9. I've spent days trying to figure it out, no joy. Same conclusion as you, it's completely random.
It seems lots of folk are hoping that 9.2 will sort things out for them - I guess Apple are also hoping for the same.