kabudasa - Just to clarify what the others have said:
The AI behavior you're seeing, which you've interpreted as "the AI resigning", is actually three separate things:
The AI no longer fighting
GlobalLOS being activated ("overwhelming numerical advantage")
The game ending before you've killed every last AI unit
The first - the AI no longer fighting - is not true. The AI continues to fight as well as it can until the game ends; it's just that the Beginner AI and many of the others as well deliberately don't fight very effectively at all. They are very passive from the start of the game and remain passive until the game ends. If you want an AI that puts up a fight you'll need to start playing against the more difficult AI settings.
The second - GlobalLOS being activated - happens in all games, regardless of which AI you're playing against, and in fact also happens in multiplayer games without AI (other than FFA). As GoogleFrog said, this feature is in place to prevent games from dragging out forever. It gets activated when one side has 25x the army value of the other side. The AI doesn't change its behavior when this gets activated; it continues to fight as well as it is able to. It just allows you to more easily dispatch the AI by finding the last constructor hiding in some far-off corner that your radar doesn't cover.
It looks like GoogleFrog recently added a modoption to disable this, so if you don't like this feature you'll be able to disable it after the next game update is pushed out.
The third - ending the game without killing all the enemy units - is the AI actually
resigning. The AI will resign and thereby end the game (as opposed to simply stopping fighting, which it never does) when it has no constructors and no factories. This was added because it seemed like a pretty reasonable end-of-game condition for typical skirmish games; as long as there's at least a single constructor it's conceivable that the AI could come back from behind, but if the AI has no factories or constructors it has no way of producing more units and can only win the game if it can destroy the player using only its current army - which is very unlikely.
This means that if you really do want to hunt down every last AI Flea and Razor without the AI quitting on you, you'll either need to carefully allow one enemy constructor to survive, or set the disableAiTeamResign modoption to 1.
Hope this helps with what you're trying to do!