[Alneyan]

The Planetary Bombs (Resupply Depot/Spaceport) can take down a homeworld, since it has these two abilities. One hit is enough, if the planet is not shielded. All facilities can be destroyed because of weapon fire; the amount of damage needed in AIC should be higher than in stock, but it can still happen.

So, if there were battles and your planetary shields went down, facilities are relatively easy to destroy. If there were no battles, intelligence projects can destroy facilities, but you should have got a message in this case.