It sadly got left hanging when Malibu Comics went under, but they had two parallel miniseries started after T2 came out: Nuclear Twilight (the future war) and Cybernetic Dawn (picked up right after the movie). In the latter, as the Connors and remaining Dysons are heading away from LA, John muses out loud that something's been bugging him. If they stopped Skynet from happening, how come it had all still happened? How come they all remembered it? If they
had prevented Skynet, he wouldn't be there, there would have been no Terminators, and so forth. I think everyone forgot about the arm Arnie left in the machinery. I like your theory that everything continued -- just got set back a little.
Dark Horse and Malibu both maintained that other Terminators had come through (Dark Hose had, among other things, the aptly-titled "Secondary Objectives" miniseries, for instance), and Malibu showed us Skynet's early temporal-displacement failures that the government had been collecting -- Terminators that had materialized partially in walls, and such.
My big thing is in this, in Star Trek, in Babylon 5, in Back to the Future, etc., the "recursion paradox". *sigh* I get
so tired of it. It's not a logic puzzle or a simple engineering challenge. Paradox means reality is not so arranged as to allow that thing to happen. You can't have the situation in Terminator: John Connor, son of Sarah Connor, is rallying humanity against the machines and turning the tide of the war, so Skynet sends a Terminator back to kill Sarah before John is even conceived. (As a computer, Skynet should know this is impossible). John sends his father back to stop the Terminator and make sure he himself is conceived in the first place. But then you start running into all the temporal problems. The "first time through", there was no Terminator to donate an arm and CPU to make Skynet happen in the first place. Sarah had an uneventful job as a waitress and a roommate with an annoying boyfriend. None of the catalysts are present.
Unless we treat this as a nexus point. By whatever mechanism, Skynet
has to happen,
a John Connor
has to be born, temporal-displacement technology
has to be invented. Then the series becomes more about fiddling the variables. Maybe first time through Sarah met someone some time later than the first film's timeframe and had a son by him who she named John, and Skynet happened way later. And what we saw in the first movie was just one of a near-infinite number of instances, Groundhog Day style -- Skynet attempted to prevent humanity from bouncing back to gain advantage in the war, and that kicked everything off. Every attempt has consequences that propagate. Now Skynet happens earlier, but John Connor has a different father and is also born earlier. What if there's one or two more iterations between the first and second film, so that by that point John is born even earlier (1981 instead of 1985) so the math works. And since each attempt alters things for Skynet, too, it has no memory that it made an attempt, so each time is that version of Skynet's first try to swing things in its favor.
Grist for the mill...
--Jonah