I lost the first battle three times. When I did get past it, I bought three more ships, then lost the next battle. I'm beginning to suspect there's more to battles than simply putting the right ship in the right spot and watching it get shot to oblivion.
It would be nice if the pop-ups went away when you activated them (clicking "Mine" or whatever), and if they didn't appear at all when you returned to a place where the resource is already spent.