What's with the monsters at the Black Omen? You can go through it three times if you start in 1000 A.D. and work backwards, yet some monsters you can only fight once. And what's with the souped up Lavos spawn?
The enemies in question are the Lavos spawn, the Mutants, and the Laser Guards on the outside. In all probability, their disappearance after one battle is a result of their event programming; as bosses, they were given this condition without a second thought. However, a viable plot solution does exist. Notice that the Lavos spawn and the Mutants all seem to unnaturally appear; the Lavos spawn even comes out of a Gate. This means that they were not always present on the Black Omen, and instead came from somewhere else (for instance, the spawn may have come from 2300 A.D. at Death Peak). In this case, they could only travel to the Black Omen once; if they were defeated, that's it -- they've exited their home periods and died, leaving no further versions. This theory only encounters a problem with the Laser Guards, who exist normally on the outside of the Omen and do not appear after being defeated once.
Concerning the Lavos spawn, it is interesting to note that it is considerably stronger than the ones encountered on Death Peak. This is most likely due to the time that has passed since the heroes ascended the mountain. In the future, the Black Omen could take the strongest spawn to have matured thus far and transport it to fight the party. This is also consistent with the theory of a one-shot transport above; until the Black Omen were defeated once, it would still exist in the future.
This still leaves a problem. Unless the Black Omen exists in a state of Time Error (and since the villagers comment on it and it seems to float as if passing normal time), it would be impossible for Queen Zeal to summon a Lavos Spawn from 2300 A.D., when that era is effectively in the future and has not happened yet. This breaks the temporal internal consistency of the game. Thanks to Berf for pointing this out. A few theories have been put forth:
The only explanation I can think of is dramatic coincidence. Basically, while the party is out doing sidequests but before Lavos is defeated, Queen Zeal, hoping to improve the Black Omen's defences, summons a Lavos spawn from the future. This works because the future is still ruined and it isn't far-fetched to think she would enlist extra-temporal help to defend the Omen. From now on, the spawn's appearance in 12'000 BC is protected by time traveller's immunity regardless of the state of the future. The problem is, because she's proactively summoning the spawn rather than reacting against the party's assault, the specific chamber and moment she summons the Lavos spawn are essentially arbitrary. Yet the party encounter the spawn at precisely the right place at precisely the right time to see it just coming out of the Gate, a huge coincidence for which the only explanation is "rule of drama".
There is also the possibility that the spawns have existed since Lavos first arrived in the planet...Lavos's spawn are his offspring that are being nurtured from the moment Lavos was born with asexual reproductive capability. Queen Zeal, in raising the Black Omen in 12,000 B.C., may have taken one of these spawn from Lavos at the time (through some kind of transporting magic) to be a personal defender for the Black Omen.
Unresolved Flow Principle
I thought hard about this, and I'm guessing that Flow Principle might cover it. While it's true that Crono's going to defeat Lavos, as long as it hasn't happened yet, the "memory" of the last existing timeline (in which Lavos destroys the earth) would still be active. Queen Zeal should be able to reach into it.
Still, this is just problematic all the way around. Nothing else in the series touches upon "summoning" something from the future, or having a window into it. We ran into this problem with Chrono Cross, with Chronopolis's existence in the Sea of Eden as part of the El Nido archipelago. This is by no means an acceptable answer, leaving this an unresolved issue.