Cotal:
The answer to desabilization is a combination of the following:
a) High Morale - since destabilization acts to lower morale and attempt to force planets into defection through failure of loyalty checks (see Brad's article on Sector Influence in the Encyclopedia), keeping morales above 80 will generally limit its effectiveness. (To defect, planets must fail 2 loyalty checks against their Morale in a row.)
To accomplish this, lower taxes and build +Morale planetary improvements. Also, stationing combat vessels in orbit helps, since the system defense strength (= to the modified combined AF+DF of those vessels) positively modifies the system's morale in your favor.
Resistance - A key factor in defection is the culture ratio in the sector. Poor Morale planets will defect to a rival culture if it becomes predominant in their sector. This factor is multiplied the greater the cultural disparity: cultural differences of 3000 pts. or more will almost certainly flip the planet to the dominant Empire.
Resistance values serve to decrease or eliminate this effect. For example, in one game I "inherited" an AI planet through destabilization. However, I was outpointed in culture in that sector ~7000 to ~1600. (It was in the middle of their Empire.) Morale was set immediately to 1. No number of +Morale improvements or amount of propaganda would raise this value. However, as soon as I built a News Network (+10 resistance) and the Secret Police (+15), morale shot up to 100. No tax rate changes, TR's or ship garrison were needed.
If you are stuck at 1 morale on a planet, most likely your Resistance value is too low (or nonexistant).
c) Culture: Dominant Empires (i.e., 2x or 3x the amount of culture over any rivals) tend to shrug off destabilization in their sectors, since there is such an overwhelming amount of loyal culture being generated around all their planets. If this value is high enough, any planets which do secede may well revert back in the next couple of turns. Building Culture & Party Palaces in threatened sectors tends to suppress the risk of defection.
d) Counter-Espionage: It has been reported on the forums that counter-espionage is factored in as a defense against destabilization efforts. This is undocumented, and has not been (afaik) confirmed by the dev's.
From the above, you can draw a few corollaries about using destabilization effectively:
1) Consider destabilization an adjunct to your other efforts, not an offensive strategy in and of itself. Destabilization serves to force the target AI to spend money on infrastructure it otherwise wouldn't build, verses bulking up its military to fight you. Destabilize in concert with a general program of culture-bombing. Use Culture & Party Palaces to establish cultural parity or dominance in a sector in conjunction with your destabilization expenditures;
2) Maximize influence resources. Since culture dominance is an important factor of defection, raising this bonus will assist your destabilization efforts and benefit your expenditures;
3) Invade destabilized planets having weakened Morales using Information Warfare. The dissaffected population amount will not add to the planet's defense (i.e., will not fight) but will, instead, join your Empire as the planet's base populace once captured. This will improve your combat odds, lower your casualties, increase your starting populace, and thus serve as a good culture-producing base in the midst of the opposing Empire;
#7 Sephlock: The AI's building strategy varies by Empire. Torians and Altarians build almost everything. However, the Yor are stingy, and the Drengin are downright Mongolian, emphasizing warships over improvements. Destabilization is thus more effective against the latter, catching them unprepared and forcing them to divert funds to +Morale/Resistance improvements.
#10, 13 Gerakken, Omega: The AI has gotten much better at handling poison pills in 1.05. This was one of my favorite tactics in 1.03 & 1.03. However, now the AI will merely build a colony ship/TR and embark excess population, or build the necessary social improvements.
I have concluded that you're just better off, for VP conditions, keeping your planets or invading about 10-20 turns later to take it back; the population is worth more than the money in MV submissions.
~SDC~
Stardock Forums
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Resistance - A key factor in defection is the culture ratio in the sector. Poor Morale planets will defect to a rival culture if it becomes predominant in their sector. This factor is multiplied the greater the cultural disparity: cultural differences of 3000 pts. or more will almost certainly flip the planet to the dominant Empire.