I have the US version of the Note II for Sprint (SPH-L900.9), bought early 2013, rooted with a custom ROM, and I thought mine was experiencing the SDS (sudden death syndrome) also. I came home from work to find that my phone's battery had died, so I plugged it in to charge & when I went to turn it on, it booted through the ROM splash screen & turned off. If I took the battery out & put it back, it would repeat this process, but never get any further & it was no longer showing up on my laptop's Explorer list or under Kies. I noticed that the top half was getting warm & if I left it unplugged, it would go dead pretty quickly. It would also not react to any button presses, unless I took the battery out & reinserted it, at which point I could get it to reboot, but only to the point that the ROM splash screen went off (where the main portion of the boot process takes place, apparently).

I could get it to boot into TWRP recovery, but short of doing a factory reset, nothing seemed to restore the phone, including reflashing the ROM & clearing the cache/dalvik cache, but I noticed it wasn't mounting the external SD card (64 GB SDXC), so I couldn't backup the data before doing a factory reset.
So, I took an 8 GB SD card from another phone, made enough free space & was able to backup the data & system & do a factory reset. If I reset the phone & restored anything (even just the data, not the system), the problem repeated itself. If I did a clean reinstall from a factory reset (through TWRP recovery), I was up & running again. Thank the Gods I have my contacts syncing thru Google & my pictures automatically uploading to Dropbox & all my notes are in Springpad - at least my most important data is recoverable! Good luck to anyone else out there experiencing these mysterious 'blackouts' on their Note II...