I see you are using LP5 kernel
What rom are you on now ?
Auto shutdown when phone idle could be due to :
1. Kernel incompatible
2. Modem incompatible
3. Apps incompatiblity ( especially certain crack/pirated apps often cause such issues )
You have to do own test /experiment to identify source of problem. There is no one correct answer
However based on what I ahvce read at XDA of users experiences, it is unlikely LP5 kernel issue - kernel issue was a probable cause only on LP1 kernels, not on LP5 or even LP6 kernel
Changing modems help as my personal experience in using the earlier ICS roms ( based on LP1 ) shows that using LB2 eliminate such issues - before that I was using LP1 modem
Apps - you evaluate yourself what type of apps you have
I'm using Stunner rom .19. I'll keep monitor especially for the apps incompatible issue. Anyway, I also having difficulty connect Wifi which my stock rom don't have this issue.