Unit bar disappears when you have too many minions.
Most easily seen if you build one of every room and convert a few Empire units. I'm not sure the exact number of minions required, but eventually the entire unit bar vanishes and the only way to pick up units is to use hotkeys.
See picture here: http://steamcommunity.com/id/ArtixFox/screenshot/266093048581678006
You can see that the "close quickbar" arrows are floating off on the bottom right of the screen, so there should be unit portraits between it and the Workers portrait. Happens in any map or campaign mission that you can get enough minions in.
Game Version:
Steam Public
Platform:
Windows
Indeed 4:3 is not very common today, but I faked this resolution and was able to replicate the issue.
Now we made it screen ratio dynamic, which means it will just show less or more units at once depending on screen ratio and HUD Scale, to prevent it to be bigger than the screen and thus being fully omitted.
The issue will be fixed in next patch :)