And here I was, going to bow out.

I think that there is a misunderstanding about what the word stability means. Mixing hydrogen and oxygen is a stable process, until a spark initiates a chemical reaction. Hydrogen is stable, as is oxygen.

In the case of matter and antimatter, they are both utterly (as best as the best physicists in the world can measure) stable. However, they do annihilate each other.

Since matter is easy to come by, the trick is to (a) generate antimatter, (b) keep it in a vacuum, removed from all matter. This could be done by putting it in a vacuum vessel and suspend it using electric or magnetic fields (c.f. modern particle physics beams or E.E. Doc Smith's anti-iron). Alternatively, one could isolate antimatter in deep space. Note that orbiting the sun wouldn't work, as the protons in the solar wind would annihilate the antiprotons in the antimatter, and the result would be an impressive energy source.

Regarding antimatter as an energy source on earth, there are two problems. One is that it is exceedingly dangerous. A single gram (one paperclip) of antimatter, coming in contact with a like amount of matter, has an energy release comparable to the first several nuclear detonations. So your containment vessel must be fool-proof.

The other problem is that you have to manufacture antimatter. You can't just go and mine it or something. In the course of manufacturing antimatter, you use FAR, FAR more energy to generate it than the antimatter itself contains. That energy could be used to heat houses, etc. The process of generating antimatter, just to use it for energy generation is dreadfully inefficient. Worse than government bureaucracy....

Thus antimatter has two "practical" purposes. One is extraordinary weapons. The other is when energy requirements are large and space is small. This might be on a satellite and/or spaceship. Since nuclear and/or solar power suffices for most satellite purposes, probably only some hypothetical spaceship might use it. And before one goes off into science fiction, there are real technical issues involved in such an attempt (i.e. propulsion mass, danger of the antimatter touching matter, etc.) The impracticality is the extraordinary difficulty in procuring some. After 30 years generating "vast" quantities of antimatter, we have generated only enough to warm a 20 oz cup of coffee from room temperature to something approaching drinkable.

At any rate, antimatter is stable. Dangerous as hell (in principle, not yet in practice), but stable.