Only the events of the first game actually happened, and each sequel is an exaggerated retelling.
Why does Morden keep falling for the Martians' plots? Why do the Rebels never drop their vendetta no matter how many common enemies they have with the Regular Army? Why won't Allen stay dead? The answer is simple: Each new game in the series is the same story, as told by a new generation that never actually saw the original events.
- Well when Morden fell for the Martians plans in the second game, this was the first time he had joined up with him. In the third game, Morden was kidnapped and had no plans to join up with the Martians. His soldiers had no idea the Martians were even behind this. Also, in the fourth and fifth games, Morden wasn't even the main antagonist. In the sixth game, the Martians probably didn't rebel against him because they were trying to protect themselves from the Venusians, and if they rebelled, they knew they were going to get their butts handed to them. However, I'm not sure why Allen is still alive after all of this. Word of God says it's because of his commitment towards his family, but that's kind of stretching it. But then again, the series doesn't take itself very seriously most of the time, so I guess we could stretch our suspension of disbelief. I see where you're coming from, and it's a pretty good theory, but the evidence against it is already in front of you.
The Regular Army protagonists are connected to a Respawn
That's why they can always come back after so many deaths. The Rebel Army managed to get one too, but it an inferior version and they only 'connected' it to Allen due to said inferiorities, and thus that's why he always comes back as well.