This happens in the "Heavy Metal" mission so I know it's nothing to do with my mission as such but it's very annoying. Perhaps it's a bug, I don't remember this happening when I played OFP a couple of years ago.
You did imply that you "should" have the ability to call for support? Even though it makes sense that the group commander of the vehicle would be the one to.
I've been messing around with the Addons and the Config.cpp, you can add your own actions that way.
But if your willing to use the action menu to make the call yourself, instead of the group commander. Then there is not much difference in using a standard radio call, Other than aesthetics?
You could enable the radio option when your vehicle reaches a certain level of damage, so at least you would not be looking at it all the time?
What doesn't make sense when you have an AI commander is that you can report other things that you need apart from repairs to the vehicle.
If the AI commander is not in the same vehicle, then you would use the radio, or shout very loud
Otherwise it's up to him to make the call, privilege of rank and all that.