One of my colonies was hit hard by an alien attack. Although I successfully defended it, the population was reduced to just under 450. After rebuilding everything, that number has held steady... but it's not going back up, and those messages are becoming annoying. What can I do about this?

Make the tax to zero.

drop taxes & power down all buildings (like factories or Research,....
concentrate on the basic needs of the populus
livingspace
hospital
foods
power
if either of those aren't in the green you face losing the planet soon.

then with a minimal investment, start adding morale buildings like church and bar
(if you're in dire need for credits, consider demolishing tech centers in the early game, when u demo a 100% HP building u get 30% of it's credit cost for scrapping it.
and don't forget to place an extra barracks built adjacent to your biggest powerplants so you can store more tanks for defense

population number should start booming soon enough, but it takes a while.
after a while raise taxes a bit while keeping them all happy and breeding.

so when the pop is increased and the basics are manned 100% and u have surolus workforce
turn on buildings and see how for you get .... rest is self explenatory.

and once you got a good population number, always remembern happy people pay taxes and the police can convinve some of the other onces too.