Allegiance drops to as low as 25% based on distance from your capital, and for TEC you can only get +10% from culture. For a sufficient distance from your capital, less than 50% loyalty is very normal. However, if it's close in proximity to your capital, there is only one culprit: enemy culture. This can reduce the loyalty of any of your planets, and if loyalty reaches zero you lose control of the planet completely as if it was bombed out. To fight enemy culture, you need culture of your own, and that means building broadcast centers as TEC.
As far as your Novalith goes, you lose the ability to shoot if you no longer have 8 military labs. I'm suspecting based on what you're saying that your empire is actually very small (maybe only 5 or 6 planets) and you barely have enough room for all your labs and factories, let alone broadcast centers, trade ports, and refineries. Normally such small empires have no business with Novalith Cannons or other high-level technologies, and you'd be much better served by a conventional military.
