I'm not sure. It may be that the increase in morale is causing a bump in population, causing just enough overcrowding to bring the morale back down. I've noticed the same thing when I put starbases on the morale-improving resources or upgraded those starbases. If that is what's happening, it's happening *FAST*, however. I added two mining upgrades to two morale-boosting starbases in one turn, and two turns later, my morale was right back where it was. Between the two starbases and all the morale-boosting anomolies I found, I'm probably at at least a 40-50% morale bonus, but it sure doesn't feel like it. And I'm the populist party, so there's another morale bonus.
It's possible that a major power is destabilizing me, but in my current game, the only races that might have anything against me are struggling to exist, and if someone like that can afford to cause this much problem to someone so much larger than they are through destabilization, then destabilization isn't play-balanced. Also, I think that if this were the case, the game should do like MoO3 does, and tell me that someone is causing unrest, without telling me who.