Don;t know about the K800i but I had the same problem with an SE T630 and SEK750i. I found that the battery was a bit loose on both of them and simply folded a bit of paper into the battery compartment to keep it held in place (I know you shouldn't have to do this, but...).
Anyway, on both phones it cured the problem and it did not switch off (unless I dropped the phone).
I've got the W880i and not had the problem, but noticed that the battery is held in place a lot firmer than previous SE phones.
It maybe worth looking to see whether this is the problem.
Mind you, if it is only one month old you could get it checked under warranty.
Regards
kfv