After the 1.66 update, this issue does not longer appear for us. Everything is showing 10/10 running:
Arma3: 1.66.139494
CBA: 3.1.2.161105
ALiVE: 1.2.2.1611241

Clarification: running the same combination but with A3 1.64.whatevs-Stable still produced the error. It was right after the upgrade the error automagically vanished.

yay! :)

Finally got my thumb out of my posterior and made a repro mission, sorry for the delay.
CBA 3.1.2.161105
ALiVE 1.2.2.1611141

Mission file: https://dl.dropboxusercontent.com/u/4170539/arma3/CO04_Alive_Test.Stratis.pbo (select Group Leader for ALiVE_tablet in backpack)
Server rpt: https://dl.dropboxusercontent.com/u/4170539/arma3/arma3server_2016-11-16_18-37-54.rpt

Works 10/10 in SP and Local MP, for me the UH80's disappear under Transport but shows under CAS.

Thanks for the quick replies!
I'll gladly admit that I haven't tried it with just ALiVE and CBA. I'll see if I can get some spare time tomorrow evening (Europe time) and create a new mission tomorrow replicating as much as can be done without all the other mods' modules that I can from the current mission and see where it leads me. Then I'll reply if I find anything.
Thanks again!

I'm having this issue aswell, but it appeared when updating from 1.2.0 to 1.2.2, so no copy & paste.
All Combat Support units are placed using the "advanced" method and I've tried replacing the main Player Combat Support module with no effect. After that I tried replacing the C2ISTAR module to no effect either.
Then I replaced all helicopters and artillery pieces and it basically just shifted which ones that did not show.

All my units are RHS units, but it didn't do any difference if deleting them and placing vanilla units instead.

All units are synced to both PCS and Virtual AI modules (due to the synced units not being virtualized setting).

Anyone got any ideas on what I can try next? :)