I searched a lot about this problem. A lot seem to have this problem with Kitkat roms but I have yet to find a solution. Whattsapp, telegram, hangouts and email also dont arrive when screen is off. I have wifi set to Always on.
I tried Neatrom AOSP and Slimsaber, they both have the same problem (same source) On JB this problem wasnt there. Tried everything from changing kernels to wiping caches, complete wipes and installs. Fresh install of whattsapp, all does nothing to the problem. If I turn on and unlock my Phone messages will arrive, sometimes after 1 minute.
Push notifier app doesnt work, tried it already. I havent greenified those apps. And have reflashed at least more than 10 times. Complete wipes and fresh download of whattsapp. I can see in my router that my Phone keeps its connection during sleep.
Both wifi and 3g tiles are orange most of the time, thats also weird. Some say its like that but Ive checked some phones and they dont do that.