I finally have an assumption, what the problem can be.
There seems to be a counter for the number of power plants you already have deployed (or can deploy). It is shown as a “stack” of cards for power plants in the lower left corner. Stack is reduced when a power plant is deployed and incremented if one is destroyed.
For 1vs1 battles these is working great. The power plant card stack is reduced by one card if you are built one plant and it is going away completely if you built your three plants (shows “max” instead). If a plant is destroyed, the stack comes back.
For 2vs2 battles the mechanism is buggy.
So sometimes (or often) my card stack is not reduced if my battle partner built a plant. So even if all three plants are built, I still see the card stack and it seems, that I can deploy another power plant card but it always shows “invalid placement” if I try to deploy it somewhere.
Sometimes the stack goes away like it should and shows “max”. But most time it is not working properly.
I assume, there is a syncing problem between the two counters of both participants as partners for the 2vs2 battles. This ends up in the problem described at first by me and in the other problems with the power plants.
Maybe your devs can watch over this and find the issue now