Can't destroy the asteroid base?

I am on the asteroid base mission, but I have encountered a problem. The Carrier has been destroyed and the longbows fired torpedoes into the Asteroid base until it reached 34% health... and now nothing.

They just fly around randomly while asteroid fighters keep spawning. What is wrong?

use your guns

I did, finally, but it took forever. These shields on that base are absurdly strong.

also start pounding the carrier before it powers up to give the torpedoes less to shoot at

... in the hangar bay...

The quickest way to pass that mission is to destroy the weapons subsystems and then simply cover the Longbows. Remember that they will try to evade while under enemy fire and will not use their torpedoes.