It's an escort mission, as per the mission instructions: "Defend" Mission Protect Gaia. You have to keep the escortee from getting killed until time runs out. Unless you bugged out, you didn't run out of time, you let the escortee die. (It's always worked fine for me)
And fwiw, Unless you're really into micromanagement, my experience is melee units are pretty much completely worthless. They'll frequently just stand there, even if an enemy is 2 pixels out of range shooting at 'em. 4 ranged units is the way to go unless you want to be constantly picking up the melee's and dropping 'em on an enemy.