Are you fighting the Manti? They get fighters to protect their worlds. If you kill them, they respawn another set in 2 turns. This can interrupt planet invasions. I think the devs are going to remove it or something because its too powerful.
To take their colony worlds, you need to attack with 2 separate fleets, one to kill the defending ships and another to invade the colony. You could try invading with one fleet, but it won't work because the attacking fleet would waste a turn killing the ships, thus leaving a 1 turn window to act (which won't be enough).
Its impossible to take their core worlds because you need 5 turns to invade them, but their fighters respawn in 2.
Edit: I just checked your save. The Iconians also get the paranoid ability. They had it back in GalCiv 3 when planet invasions didn't take multiple turns.
This can't possibly be working as intended because it takes so long to besiege. I have no issue with the paranoid ability. It is perfectly fair that I lost a relatively puny ship attacking a colony that was only defended by drones. However, it is madness that the drones would interrupt a siege that is in progress. A free attack on the invaders? Sure. But an interrupt? No way.
Edit: You are right that as it currently stands, you need two separate attacking ships to besiege a paranoid colony planet. However, it does not appear that the AI is subject to the same interrupt. Their siege of New Iconia is still underway.
