The problem is probably due to cultural influence and morale. If the Independent League is generating the most about of cultural influences in sectors your planets are located in, your planets will be in trouble, morale will plummet, and they will switch allegiance.
Galciv and Altarian prophecy are a game about starbases, literally. Google around for strategy guides at fan sites. People have figured out crazy formulas for generating huge amount of cash from trade modules on starbases. Cultural modules on starbases can also significantly boost your influences...
Mostly, you want to be a dealer in technologies. You want to be especially supportive of neutral players, selling them techs, giving them ships... Help them stay in the game and let them help keep other AIs busy and not attacking you. You can VERY significantly boost your cash income this way, which you can plow back into your own research and empire-building.
When you set up the game, get the speed boost. AIs do know from the beginning where all the high quality planets are, and so you can really use that speed boost to have as much chances of grabbing those HQ planets. A class 19 is probably worth 3 or 4 class 15 planets, if not even more.