Update time:
I heard back again from JT saying request a refund from your supplier, if they're no help fill in this form and send it to us. So that's something. I think there's a bit of a language barrier at JT, I don't think anyone reads english well enough to reply the detailed emails they're getting about the issues.
For those still having issues, I got a little glimmer of hope from madboy over on the evic forum:
Have you tried re-flashing the firmware? Upload a new firmware image http://www.joyetech.com/mvr-software/?sid=155 (just to ensure that the one you originally downloaded is not corrupt) Downgrade the firmware to say 1.1 (with the battery out), then put the battery back in. Take the USB lead out of the Mini. Remove tank, press the fire button a couple of times. Remove battery. Now re-flash the firmware to 1.2. Put battery back in and see what happens.
I hadn't previously been able to flash without the battery in but it worked this time although I got some checksum errors. Despite those errors the unit seems to not be having the sleep issues although I didn't test it extensively with Ti, I've been on SS coils now for a while and whilst there's not a lot of temp control with SS (210f too cool, 220f too warm) it's pretty reliable so that what I'm sticking with until JT release a SS profile in an update.