Same problem here. Black screen on Doubleshot with CM 10.1. Made me really concerned when it happened, as I was was reading the hardware maintenance thread earlier today (for fun) so I thought the LCD went.
This is the first time this has happened in the three weeks I had this phone, and I've been on 10.1 for almost a week now.
Because battery life is an issue for me as well, I edged things up only slightly (from 96 MHz to 128), hopefully that will do to the trick. If not, I will try 192 MHz.
 Speaking of which, any tricks on keeping battery usage low? I use Deep Sleep Battery Saver which helps out a lot. And I'm selective about my apps (removed Songza because it was hanging around while closed, eating up battery life). GPS stays off, although I keep Wi-Fi and 3G on. It looks like the screen becomes the biggest draw at this point. Any advice would be appreciated.
Primary Phone: HTC MyTouch 4G Slide (Doubleshot) running CyanogenMod 10.1
Backup Phone: Samsung Infuse 4G (i997R) running CyanogenMod 10.1