I've been doing some experimentation and maybe figured it out, at least with my phone.

On AT&T in the US, if you have an LTE data plan, you have access to an alternate APN. It's actually the only preloaded APN on AT&T-branded LTE phones, and CM9 and CM10 use it as the default on this phone. When I switch the phone to use the old 3G/HSPA+ APN, notifications seem to be getting through with the screen off.

I don't really know what to make of this finding. Perhaps when on the LTE APN, the phone uses more juice and goes into some hibernation mode? There is no selection for that kind of behavior in CM that I can see, so hopefully this is tweaked over time.

Maybe there is a problem with the LTE APN itself or maybe the way the phone hunts for LTE signal? My area is mostly HSPA+, but I have tasted LTE over the weekend. Hopefully I won't have to keep it disabled for too much longer: